key: cord-0334801-12vfd1jk
authors: Lam, Yi Hua; Liu, Zi Xin; Heger, Alexander; Lu, Ning; Jacobs, Adam Michael; Johnston, Zac
title: The Impact of the New $^{65!}$As(p,$gamma$)$^{66!}$Se Reaction Rate on the Two-Proton Sequential Capture of $^{64}!$Ge, Weak GeAs Cycles, and Type-I X-Ray Bursts such as the Clocked Burster GS 1826$-$24
date: 2021-10-26
journal: nan
DOI: 10.3847/1538-4357/ac4d8b
sha: cb1b2dbf7c8f43042f46edba95ecafc61adfe003
doc_id: 334801
cord_uid: 12vfd1jk

We re-assess $^{65}$As(p,$gamma$)$^{66}$Se reaction rates based on a set of proton thresholds of $^{66}$Se, $S_mathrm{p}$($^{66}$Se), estimated from the experimental mirror nuclear masses, theoretical mirror displacement energies, and full $pf$-model space shell-model calculation. The self-consistent relativistic Hartree-Bogoliubov theory is employed to obtain the mirror displacement energies with much reduced uncertainty, and thus reducing the proton-threshold uncertainty up to 161 keV compared to the AME2020 evaluation. Using the simulation instantiated by the one-dimensional multi-zone hydrodynamic code, KEPLER, that closely reproduces the observed GS 1826$-$24 clocked bursts, the present forward and reverse $^{65}$As(p,$gamma$)$^{66}$Se reaction rates based on a selected $S_mathrm{p}$($^{66}$Se) = 2.469$pm$0.054 MeV, and the latest $^{22}$Mg($alpha$,p)$^{25}$Al, $^{56}$Ni(p,$gamma$)$^{57}$Cu(p,$gamma$)$^{58}$Zn, $^{55}$Ni(p,$gamma$)$^{56}$Cu, and $^{64}$Ge(p,$gamma$)$^{65}$As reaction rates, we find that though the GeAs cycles is weakly established in the rapid-proton capture process path, the $^{65}$As(p,$gamma$)$^{66}$Se reaction still strongly characterizes the burst tail end due to the two-proton sequential capture on $^{64}$Ge, not found by Cyburt et al. (2016) sensitivity study. The $^{65}$As(p,$gamma$)$^{66}$Se reaction influences the abundances of nuclei $A$ = 64, 68, 72, 76, and 80 up to a factor of 1.4. The new $S_mathrm{p}$($^{66}$Se) and the inclusion of the updated $^{22}$Mg($alpha$,p)$^{25}$Al reaction rate increases the production of $^{12}$C up to a factor of $4.5$ that is not observable and could be the main fuel for superburst. The waiting point status of and two-proton sequential capture on $^{64}$Ge, weak-cycle feature of GeAs at region heavier than $^{64}$Ge, and impact of other possible $S_mathrm{p}$($^{66}$Se) are also discussed.

During the accretion of stellar matter from a close companion by the neutron star in a low-mass X-ray binary (LMXB), the accreted stellar matter, mainly comprising H and He fuses to heavier nuclei in steady-state burning (Hansen & van Horn 1975; Schwarzschild & Härm 1965 ) and a thermonuclear runaway is likely to occur in the accreted envelope of the Corresponding authors: Yi Hua Lam, Zi Xin Liu, Alexander Heger lamyihua@impcas.ac.cn, liuzixin1908@impcas.ac.cn, alexander.heger@monash.edu neutron star. This causes the observed thermonuclear (Type-I) X-ray bursts (XRBs; Woosley & Taam 1976; Maraschi & Cavaliere 1977; Joss 1977; Lamb & Lamb 1978; Bildsten 1998) . The burst light curve, usually observed in X-rays, is the important observable indicating an episode of XRB, which can be either a series of XRBs or a single XRB, for instance, the XRBs recorded by the Rossi X-ray Timing Explorer (RXTE) Proportional Counter Array (Galloway et al. 2004 (Galloway et al. , 2008 . For a series of XRBs, we can further deduce the recurrence time between two XRBs, or the averaged recurrence time of a series of XRBs. The burst light curve profile and (averaged) recurrence time can be studied via models best matching with observations to further under-stand the role of an important reaction, e.g., see Cyburt et al. (2016) ; Meisel et al. (2018) .

In recent years, the Type-I clocked XRBs from the GS 1826−24 X-ray source (Makino et al. 1988; Tanaka et al. 1989; Ubertini et al. 1999) became the primary target of investigation due to its almost constant accretion rate and consistent light curve profile (Heger et al. 2007; Paxton et al. 2015; Meisel et al. 2018 Meisel et al. , 2019 Johnston et al. 2020; Dohi et al. 2020 Dohi et al. , 2021 . The other important feature of GS 1826−24 clocked burster is the nuclear reaction flow during its XRB onsets. It can reach up to the SnSbTe cycles according to the models (Woosley et al. 2004 ) used by Cyburt et al. (2016) and Jacobs et al. (2018) to investigate the sensitivity of reactions. The region around SnSbTe cycles was found to be the end point of nucleosynthesis of an XRB (Schatz et al. 2001) .

This state-of-the-art GS 1826−24 model was even recently advanced by the newly deduced 22 Mg(α,p) 25 Al reaction rate to match with observation (Hu et al. 2021) . As the abundances of synthesized isotopes are not observed, we remark here that using a set of high-fidelity XRB models capable to closely reproduce the observed burst light curves is important for us to diagnose the nuclear reaction flow and abundances of synthesized isotopes in the accreted envelope.

According to this GS 1826−24 model (Heger et al. 2007; Cyburt et al. 2016; Johnston et al. 2020; Jacobs et al. 2018; Hu et al. 2021; Lam et al. 2021a) , throughout the course of the XRBs of GS 1826−24 clocked burster, the nuclear reaction flow has to break out from the ZnGa cycles to reach the GeAsSe region. The reaction flow inevitably goes through the 64 Ge waiting point and also the GeAs cycles that might exist (Van Wormer et al. 1994 ) before surging through the region heavier than the Ge and Se isotopes where hydrogen is intensively burned. The GeAs cycles are supposedly weaker than the NiCu and ZnGa cycles due to the competition between the weak (p,α) and the strong (p,γ) reactions at As isotopes, see the weak GeAs I, II, and sub-II cycles presented in Fig. 1 . Thus, the establishment of the two-proton-(2p) sequential capture (hereafter 2p-capture) on 64 Ge could be crucial to draw synthesized materials to follow the 64 Ge(p,γ) 65 As(p,γ) 66 Se(β + ν) 66 As(p,γ) 67 Se(β + ν) 67 As (p,γ) 68 Se(β + ν) 68 As(p,γ) 69 Se path for the strong rp-process of hydrogen (H)-burning that happens in nuclei heavier than Se isotopes.

Recently, the role of 64 Ge as an important waiting point was questioned when the proton threshold of 65 As was experimentally deduced, opening a 2p-capture channel (Tu et al. 2011) ; its significance of an important waiting point also becomes uncertain in a study using an one-zone XRB model with the 64 Ge(p,γ) 65 As and 65 As(p,γ) 66 Se reaction rates deduced from the evaluated 65 As and 66 Se proton thresholds (Tu et al. 2011; Audi et al. 2016 ) and the full pf -model space shell-model calculation (Lam et al. 2016) . Moreover, Schatz (2006) and Schatz & Ong (2017) found that the 65 As and 66 Se masses contributed to the respective proton thresholds affect the (p,γ) reverse rate, and hence influence the modeled XRB light curves. We remark that the investigations of the role of 64 Ge as an important waiting point and the impact of 65 As and 66 Se masses were, however, based on the computationally effective zero-dimensional one-zone XRB model (Schatz & Ong 2017) with extreme parameters, i.e., very high accretion rate and very low crustal heating, of which the abundance of synthesized nuclei is only provided for a single mass zone but not along the mass coordinate in the accreted envelope. A finer parameter range can be chosen to improve the capability of one-zone XRB models in estimating the influence of a particular reaction on XRB with agreement close to onedimensional multi-zone hydrodynamic XRB model (Schatz 2021) . Notably, the hydrodynamic data generated from a more constrained one-dimensional multi-zone XRB model that is capable of reconciling theoretical light curves with observations could be beneficial for post-processing and onezone models to obtain the nuclear energy generation (XRB flux) consistent with the input hydrodynamic snapshots and to assess inventory of abundances and the reaction flow during the burst.

With the advantage of new and high intensity exotic proton-rich isotopes production and advances in experimental techniques of isochronous mass spectrometry in storage rings (Stadlmann et al. 2004; Zhang et al. 2018 ) and multireflection time-of-flight (MRTOF) mass spectrometers (Wolf et al. 2013; Dickel et al. 2015; Jesch et al. 2015; Rosenbusch et al. 2020) , the 66 Se proton threshold, S p ( 66 Se), could be more precisely determined to replace the S p ( 66 Se) = 2.010± 220 MeV predicted by AME2020 extrapolation (Kondev et al. 2021; AME2020) . The extrapolation is based on the Trend from the Mass Surface, which is weak in predicting protonrich nuclear masses due to the shell effect originated from the respective shell structure or the configuration of the ground 65 Ga 64 Ga 63 Ga 64 Ge 65 Ge 66 Ge 65 As 66 As 67 As 68 As 66 Se 67 Se 68 Se 69 Se + (p,γ) (p, ) Figure 1 . The rapid-proton capture (rp-) process path passing through the weak GeAs cycles. Waiting points are shown in red texts. The GeAs cycles are displayed as red arrows. The GeAs I cycle consists of 64 Ge(p,γ) 65 As(p,γ) 66 Se(β + ν) 66 As(p,γ) 67 Se(β + ν) 67 As(p,α) 64 Ge reactions (Van Wormer et al. 1994) , and the GeAs II cycle involves a series of 65 Ge(p,γ) 66 As(p,γ) 67 Se(β + ν) 67 As(p,γ) 68 Se(β + ν) 68 As(p,α) 65 Ge reactions. The other sub-GeAs II cycle, 64 Ge(β + ν) 64 Ga(p,γ) 65 Ge (p,γ) 66 As(p,γ) 67 Se(β + ν) 67 As(p,α) 64 Ge, may also be established. The weak (p,α) reactions are represented by thinner arrows.

state (Huang 2021) . Therefore, a set of forefront investigations on astrophysical impacts due to the forward and reverse 65 As(p,γ) 66 Se reactions based on a set of S p ( 66 Se) with lower uncertainty than the one predicted by AME2020 and XRB models best matching with observation is highly desired.

In this work, in Section 2, we present the formalism obtaining the forward and reverse 65 As(p,γ) 66 Se reaction rates, and discuss these newly deduced forward and reverse reaction rates. We then employ the one-dimensional multi-zone hydrodynamic KEPLER code (Weaver et al. 1978; Woosley et al. 2004; Heger et al. 2007 ) to instantiate XRB simulations that produce a set of XRB episodes matched with the GS 1826−24 clocked burster with the newly deduced 65 As(p,γ) 66 Se forward and reverse reaction rates. Other recently updated reaction rates, i.e., 55 Ni(p,γ) 56 Cu (Valverde et al. 2019) , 56 Ni(p,γ) 57 Cu (Kahl et al. 2019) , 57 Cu(p,γ) 58 Zn (Lam et al. 2021a) , and 64 Ge(p,γ) 65 As (Lam et al. 2016) around the historic 56 Ni and 64 Ge waiting points, and 22 Mg(α,p) 25 Al (Hu et al. 2021) at the important 22 Mg branch point are also taken into account.

In Section 3, we study the influence of these 65 As(p,γ) 66 Se forward and reverse rates, and also investigate the influence of the 2p-capture on 64 Ge and GeAs cycles on XRB light curves, on the rp-process path during the thermonuclear runaway of the GS 1826−24 clocked XRBs, and on the nucleosyntheses in and evolution of the accreted envelope along the mass coordinate for nuclei of mass A = 59, . . . , 68. The conclusions of this work are given in Section 4.

We deduce the S p ( 66 Se) value based on the experimental 66 Ge mirror mass and theoretical Coulomb displacement energy (and the term should be replaced as "mirror displacement energy" due to the important role of isospin nonconserving forces from nuclear origin (Zuker et al. 2002) ). The mirror displacement energy (MDE) is obtained from the self-consistent relativistic Hartree-Bogoliubov (RHB) theory (Kucharek & Ring 1991; Ring 1996; Meng & Ring 1996; Pöschl et al. 1997) . The MDE for a given pair of mirror nuclei is expressed as (Brown et al. 2000 (Brown et al. , 2002 Zuker et al. 2002 )

where A is the nuclear mass number and I is the isospin, BE(A, I < z ) and BE(A, I > z ) are the binding energies of the proton and neutron rich nuclei, respectively. We implement the explicit density-dependent meson-nucleon couplings (DD-ME2) effective interaction (Lalazissis et al. 2005) in RHB calculations to obtain the MDE(A, I) of I = 1/2, 1, 3/2, and 2, A = 41 -75 mirror nuclei. In order to constrict the complicated problem of a cut-off at large energies inherent in the zero range pairing forces, a separable form of the finite range Gogny pairing interaction is adopted (Tian et al. 2009 ). To describe the nuclear structure in odd-N and/or odd-Z nuclei, we take into account of the blocking effects of the unpaired nucleon(s). The ground state of a nucleus with an odd neutron and/or proton numbers is a one-quasiparticle state, |Φ 1 = β † i b |Φ 0 , which is constructed based on the ground state of an even-even nucleus |Φ 0 , where β † is the single-nucleon creation operator and i b denotes the blocked quasiparticle state occupied by the unpaired nucleon(s). The detail description of implementing the blocking effect is explained by Ring & Schuck (1980) . Table 1 and Figure 2 present the S p ( 66 Se) values estimated from two mean field approaches, i.e., Skyrme Hartree-Fock (SHF) and RHB. For the SHF framework with the SkX csb parameters (Brown 2021; Brown et al. 2002 Brown et al. , 2000 Brown 1998) , the previously estimated S p ( 66 Se) with the AME2000 66 Ge and 65 Ge binding energies is listed in the first row of Table 1 , whereas the presently recalculated S p ( 66 Se) values with the AME2020 66 Ge and 65 Ge binding energies (Kondev et al. 2021 ) (SHF i ), or with the AME2020 66 Ge, 65 Ge, and SHF MDE A=65 (SHF ii ), are arranged in the second and third rows of Table 1 , respectively. For the RHB framework with DD-ME2 effective interaction, we deduce the S p ( 66 Se) using (I) the spherical harmonic oscillator basis and the AME2020 66 Ge binding energy and theoretical or experimental MDE A=65 (RHB Spherical i,ii ; the fourth and fifth rows in Table 1 ), (II) the axially symmetric quadrupole deformation and the AME2020 66 Ge binding energy and theoretical or experimental MDE A=65 (RHB Axial i,ii ; the sixth and seventh rows in Table 1 ).

The region around nuclei A = 65 and A = 66 is subject to deformation as found by Hilaire & Girod (2007) , however, the SHF calculations do not take deformation into account. This somehow causes the SHF MDEs having large rms deviation of around 100 keV. The S p ( 66 Se) uncertainties of the SHF calculations are larger than the RHB calculations, whereas the RHB Axial i,ii uncertainties are lower than the ones from RHB Spherical i,ii . The uncertainty (rms deviation) of MDEs from RHB Spherical i,ii suggest that refitting the SkX csb parameters and revising the blocking effect for calculating even-odd and odd-odd nuclei are likely to reduce the SHF uncertainty to around 60 keV. Nevertheless, the deformation of nuclei is not considered in both SHF and RHB Spherical i,ii calculations. The RHB Axial i,ii that take into account of deformation further alleviate the discrepancy between theoretical and experimental MDEs, and thus reducing the uncertainty of the deduced S p ( 66 Se) values. This is exhibited by comparing the RHB Axial i,ii MDE A=66 46-keV and MDE A=65 29-keV uncertainties with the 62-keV and 33-keV (RHB Spherical i,ii ) and with the 100-keV (SHF) uncertainties, see Table 1 and Fig. 2 . In additions, the RHB with DD-ME2 calculations having an advantage that the mesonnucleon effective interaction is explicitly constructed without additional extra terms as included in the SHF calculation via the SkX csb terms which have to be continually refitted with updated experiments.

For the RHB calculations, we find that the RHB MDEs coupled with highly precisely measured 66 Ge and 65 Ge binding energies yield a set of S p ( 66 Se) values with low uncertainties, i.e., 2.507±0.070 MeV and 2.469±0.054 MeV (fifth and seventh rows in Table 1 ). This indicates that the 80- (Brown 2021; Brown et al. 2002 Brown et al. , 2000 Brown 1998 ). c quoted from AME2000, which is a preliminary data set of AME2003 (Audi et al. 2003) . d quoted from AME2020 (Kondev et al. 2021 ). e relativistic Hartree-Bogoliubov (Kucharek & Ring 1991; Ring 1996; Meng & Ring 1996; Pöschl et al. 1997 ) calculations with DD-ME2 effective interaction (Lalazissis et al. 2005) , using (I) spherical harmonic oscillator basis, (II) axially symmetric quadrupole deformation. The 62-keV and 46-keV uncertainties of MDE A=66 are from the root-mean-square (rms) deviation value of comparing the theoretical and experimental MDE(A, I) values for I = 1, A = 42 -58 mirror nuclei. We apply the same procedure to quantify the 33-keV and 29-keV uncertainties for the MDE A=65 considering I = 1/2, A = 41 -75 mirror nuclei. The uncertainties of BE( 66 Se), BE( 65 As), Sp( 66 Se) are from the combination of rms deviation and the respective experimental uncertainty. keV uncertainty of 65 As binding energy is somehow large enough to influence the deduced S p ( 66 Se), see fourth and sixth rows in Table 1 and Fig. 2 , suggesting a highly precisely measured 65 As mass is demanded. Furthermore, we also find that consistently using the RHB MDEs and precisely measured 66 Ge and 65 Ge binding energies maintains the global description feature provided by the RHB framework to describe MDEs along the nuclear region with symmetric neutron-proton number. The S p ( 66 Se) of RHB listed in Table 1 is averaged to be 2.426±0.163 MeV of which its uncertainty covers all RHB central S p ( 66 Se) values (red zone in Fig. 2 ). We caution that this is an averaged S p ( 66 Se) from two sets of independent RHB frameworks. The S p ( 66 Se) of SHF (Table 1) is averaged to be 2.323±0.241 MeV, or to be 2.269±0.193 MeV if we only consider the S p ( 66 Se) of SHF i and SHF ii . Nevertheless, the uncertainties of both averaged S p ( 66 Se) of SHF framework are still larger than the one from RHB. The S p ( 66 Se) with the lowest uncertainty among all estimations is 2.469±0.054 MeV, estimated from the RHB Axial ii , and is up to 90 keV lower than the ones proposed by the SHF. With the advantage of the consideration of axial deformation and low uncertainty, hereafter, we select S p ( 66 Se) = 2.469±54 keV as our reference. This selection also maintains the global description of MDEs provided by RHB and refrains the influence of high uncertainty 65 As mass. We present the influence of the selected S p ( 66 Se) on the 65 As(p,γ) 66 Se forward and reverse reaction rates and on the GS 1826−24 clocked XRBs. We qualitatively discuss the estimated influence from other S p ( 66 Se) listed in Table 1 as well in the following discussion and Section 3.

With using the selected S p ( 66 Se), the resonant energies correspond to the new Gamow window are shifted up to E res = 2.40 -4.70 MeV, and the dominant resonance states are shifted to the excited state region of E x ∼3.50 MeV accordingly. As an assignment of a 2.1 % uncertainty does not produce a large impact on the final uncertainty, for the present work, we extend the present uncertainty of S p ( 66 Se) to 100 keV as proposed by Brown et al. (2002) and by the S p ( 66 Se) uncertainty based on the RHB with DD-ME2 using spherical harmonic oscillator basis (fourth row in Table 1). Such extended uncertainty could be more reasonable and more conservative for us to estimate the uncertainty of the 65 As(p,γ) 66 Se forward and reverse reaction rates, and also to cover other reaction rates due to other S p ( 66 Se) listed in Table 1 , i.e., S p ( 66 Se) = 2.433 MeV, 2.443 MeV, and 2.507 MeV, whereas the reaction rates implement S p ( 66 Se) = 2.186 MeV, or 2.284 MeV, or 2.351 MeV are separately calculated, presented, and discussed in the following part of this Section. The averaged S p ( 66 Se) in Table 1 is 2.381 ± 0.041 MeV. The influence of S p ( 66 Se) = 2.381 ± 0.041 MeV on the 65 As(p,γ) 66 Se forward and reverse reaction rates and on XRB can be analogous to the influence of statistical model (ths8 or NON-SMOKER) 65 As(p,γ) 66 Se rate based on S p ( 66 Se) = 2.349 MeV.

Instead of scaling the rate as done by Valverde et al. (2018) , which may introduce unknown uncertainty to the reaction rate, we follow the procedure implemented by Lam et al. (2016) to obtain the new 65 As(p,γ) 66 Se reaction rate that is expressed as the sum of resonant-(res) and direct (DC) proton capture on the ground state and thermally excited states of the 65 As target nucleus (Fowler et al. 1964; Rolfs & Rodney 1988) ,

Each proton capture is weighted with its partition functions of initial and final nuclei (see Lam et al. (2016) for the detailed notation and formalism). The direct-capture rate of the 65 As(p,γ) 66 Se reaction can be neglected as its contribution to the total rate is exponentially lower than the contribution of resonant rate. The resonant rate for proton capture on a 65 As nucleus in its initial state i, in units of cm 3 s −1 mol −1 , is expressed as (Fowler et al. 1967; Rolfs & Rodney 1988; Schatz et al. 2005; Iliadis 2007) ,

where the resonance energy in the center-of-mass system is

x is the excited state energy of a state j for the 65 As+p compound nucleus system, E i is the initial state energy, E i = 0 for the capture on the ground state (g.s.) of 65 As, the 11.605 constant is in units of 10 9 K /kB, µ is the reduced mass of the entrance channel, T 9 = T 10 −9 K −1 , and ωγ is the resonance strength. We consider only up to the proton capture on the first excited state of 65 As, 5/2 − 1 , whereas the contribution from the proton capture on higher excited states of 65 As is negligible.

The nuclear structure information for the proton widths, Γ p , and gamma widths Γ γ at the Gamow window corresponding to the XRB temperature range is deduced based on the full pf -model space shell-model calculation using the KSHELL code (Shimizu et al. 2019 ) and NUSHELLX@MSU code (Brown & Rae 2014) with the GXPF1a Hamiltonian (Honma et al. 2004 (Honma et al. , 2005 . Hamiltonian matrices of dimensions up to 6.56 × 10 8 for nuclear structure properties of A = 65 and 66 have been diagonalized using the thick-restart block Lanczos method. These Γ p are mainly estimated from proton scattering cross sections in adjusted Woods-Saxon potentials that reproduce known proton energies (Brown 2014) . Alternatively, we also employ the potential barrier penetrability calculation (Van Wormer et al. 1994; Herndl et al. 1995) to estimate these Γ p . The Γ p estimated from both methods vary only up to a factor of 1.6. We only take into account the γ-decay widths from the M1 and E2 electromagnetic transitions for the resonance states as their contribution are exponentially higher than the M3 and E4 transitions.

The dominant resonances of proton captures on the ground and first excited states of 65 As are plotted in Fig. 3 , whereas Fig. 4 displays the comparison of the present (Present, hereafter) reaction rate with other available rates compiled by Cyburt et al. (2010) for JINA REACLIB v2.2, i.e., rath, rpsm, thra, laur, ths8, the previous rate (Lam et al. 2016) . The 65 As(p,γ) 66 Se forward rates generated from the S p ( 66 Se) = 2.351±0.144 MeV, 2.284±0.092 MeV, and 2.186±0.128 MeV are about a factor of 0.5 -0.8 below the Present forward rate at temperature T = 0.5 -2 GK, and are within the uncertainty zone of the Present rate, see Fig. 4 . The Present rate is up to a factor of 7 higher than the ths8 (or NON-SMOKER) rate recommended in JINA REACLIB v2.2 release. The Present uncertainty region deduced from folding the S p ( 66 Se) 100-keV uncertainty with the 200-keV uncertainty from shell-model estimated E j x (light red zone in top panel of Fig. 4 ) is reduced up to ∼1.5 order of magnitude compared to the uncertainty (green zone) in Fig. 2 of Lam et al. (2016) . This is due to the presently folded uncertainty from S p ( 66 Se) and shell-model calculation which is 129 keV lower than the folded uncertainty suggested by Lam et al. (2016) that combines the AME2012 (Audi et al. 2012 ) S p ( 66 Se) and the uncertainties of energy levels from shell-model calculation.

The Present reaction rate are presented in Table 2 and the parameters listed in Table 3 can be used to reproduce the Present centroid reaction rate with n = 191, a fitting error of 4.5 %, and an accuracy quantity of ζ = 0.003 for the temperature range from 0.1 -2 GK according to the Table 2 . Thermonuclear reaction rates of 65 As(p,γ) 66 Se. format and evaluation procedure proposed by Rauscher & Thielemann (2000) . The parameterized rate is obtained using the Computational Infrastructure for Nuclear Astrophysics (CINA; Smith et al. 2004 ). For the rate above 2 GK, we refer to statistical-model calculations to match with the Present rate, see NACRE (Angulo et al. 1999 ).

The new reverse 65 As(p,γ) 66 Se reaction rate based on the S p ( 66 Se) = 2.469 MeV is related to the respective forward reaction rate, Eq. (2), via the expression (Rauscher & Thielemann 2000; Schatz & Ong 2017) ,

where G i and G f are the partition functions of initial and final nuclei. The new reverse rates are presented in Fig. 5 , and compared with the ths8 statistical-model reverse rate. The respective uncertainty (lower and upper limits) of the Present reverse rate corresponds to the uncertainty (lower and upper limits) of the Present forward rate with the consideration of 100-keV uncertainty imposed from the present S p ( 66 Se). Although this 100-keV uncertainty is rather extreme, its range is capable to cover possible reverse rates due to other estimated S p ( 66 Se), i.e., S p ( 66 Se) = 2.433±0.144 MeV, 2.443±0.101 MeV, and 2.507±0.070 MeV, see Table 1 and 1 −2.98258 × 10 +1 −2.35942 × 10 +0 +3.94649 × 10 +0 −9.86873 × 10 +0 1.45916 × 10 −1 +1.01711 × 10 −1 2.46893 × 10 +0 2 −1.49044 × 10 +1 −3.68082 × 10 +0 +3.93081 × 10 +0 −9.86417 × 10 +0 1.55748 × 10 −1 +1.02469 × 10 −1 2.45374 × 10 +0 3 +1.29861 × 10 −1 −4.94352 × 10 +0 +7.67143 × 10 +0 −2.00710 × 10 +1 1.29501 × 10 +0 −2.73522 × 10 −2 6.16001 × 10 +0 4 +2.60957 × 10 +1 −1.04676 × 10 +1 +1.64542 × 10 +1 −4.16331 × 10 +1 3.26017 × 10 +0 −3.38444 × 10 −1 1.34811 × 10 +1 5 +3.41675 × 10 +1 −1.41042 × 10 +1 +2.12287 × 10 +1 −5.17133 × 10 +1 4.54240 × 10 +0 −3.08117 × 10 −1 1.87553 × 10 +1 NOTEa The a 0 , . . . , a 6 parameters are substituted in

+ a i 6 ln T 9 ) to reproduce the forward reaction rate with an accuracy quantity, ζ = 1 n n m=1 ( rm−fm fm ) 2 , where n is the number of data points, rm are the original Present rate calculated for each respective temperature, and fm are the fitted rate at that temperature (Rauscher & Thielemann 2000) , see text. We use KEPLER code (Weaver et al. 1978; Woosley et al. 2004; Heger et al. 2007 ) to construct the theoretical XRB models matched with the periodic XRBs, Epoch Jun 1998, of GS 1826−24 X-ray source compiled by Galloway et al. (2017) . These XRB models are fully self-consistent. The evolution of chemical inertia and hydrodynamics that power the nucleosynthesis along the rp-process path are correlated with the mutual feedback between the nuclear energy generation in the accreted envelope and the rapidly evolving astrophysical conditions. Meanwhile, KEPLER code uses an adaptive reaction network of which the relevant reactions out of the more than 6000 isotopes from JINA REACLIB v2.2 (Cyburt et al. 2010) are automatically included or discarded throughout the evolution of thermonuclear runaway in the accreted envelope.

The XRB models keep tracking the evolution of a grid of Lagrangian zones, of which each zone has its own isotopic composition and thermal properties. We use the timedependent mixing length theory (Heger et al. 2000) to describe the convection that transfers synthesized and accreted nuclei and heat between these Lagrangian zones. We remark that this important feature is not considered in zerodimensional one-zone and post-processing XRB models.

We adopt the astrophysical settings of GS 1826−24 model from Jacobs et al. (2018) to match with the observed burst light curve properties of Epoch Jun 1998. To obtain the bestmatch modeled light curve profile with the observed profile and averaged recurrence time, ∆t rec = 5.14±0.7 h, we assign the accreted 1 H, 4 He, and CNO metallicity fractions to 0.71, 0.2825, and 0.0075, respectively, whereas the accretion rate is adjusted to a factor of 0.114 of the Eddington-limited accretion rate,Ṁ Edd . This refined GS 1826−24 XRB model with the JINA REACLIB v2.2 defines the baseline model in this work. Other models that adopt the same astrophysical settings but implement the Present 65 As(p,γ) 66 Se forward and reverse rate (solid and dotted red lines in the top panel of Fig. 5 ), or the lower limit of Present 65 As(p,γ) 66 Se forward and reverse rates (lower borders of red and pink zones in the top panel of Fig. 5 We select the latest 22 Mg(α,p) 25 Al reaction rate which was experimentally deduced by Hu et al. (2021) with the important nuclear structure properties corresponding to the XRB Gamow window instead of the 22 Mg(α,p) 25 Al reaction rate deduced by Randhawa et al. (2020) via direct measurement. It is because Randhawa et al. (2020) rate was extrapolated from non-XRB energy region and may have an additional and large uncertainty that was not shown (Hu et al. 2021) . The recent direct measurement performed by Jayatissa et al. (2018) could be helpful to further constrain the 22 Mg(α,p) 25 Al reaction rate as long as the measurement directly corresponds to the XRB Gamow window.

We follow the simulation procedure implemented by Lam et al. (2021a) and Hu et al. (2021) , of which we run a series of 40 consecutive XRBs for baseline, Present § , Present ‡ , Present † models. The first 10 bursts of each model are discarded because these bursts transit from a chemically fresh envelope to an enriched envelope with burned-in burst ashes and stable burning. The burst ashes are recycled in the following burst heatings and stabilize the succeeding bursts. Therefore, we only sum up the last 30 bursts and then average them to produce a modeled burst light-curve profile. This averaging procedure was applied by Galloway et al. (2017) to yield an averaged-observed light-curve profile of Epoch Jun 1998, which was recorded by the Rossi X-ray Timing Explorer (RXTE) Proportional Counter Array (Galloway et al. 2004 (Galloway et al. , 2008 and was compiled into the Multi-Instrument Burst Archive 1 by Galloway et al. (2020) . Our averaging procedure was also implemented in the works of Lam et al. (2021a) and Hu et al. (2021) .

The observed flux, F x , is expressed as (Johnston et al. 2020 )

where L x is the burst luminosity generated from each model; d is the distance; ξ b takes into account of the possible deviation of the observed flux from an isotropic burster luminosity (Fujimoto et al. 1988; He et al. 2016) ; and the redshift, z, adjusts the light curve when transforming into an observer's frame. Assuming that the anisotropy factors of burst and persistent emissions are degenerate with distance, the d and ξ b can be combined to form the modified distance d √ ξ b . Instead of specifically selecting data close to the burst peak at t = −10 s to 40 s as done by Meisel et al. (2018) and Randhawa et al. (2020) , we impartially fit the modeled burst light curves generated from each model to the entire burst timespan of the averaged-observed light curve to avoid artifactually expanding the modeled burst light curve and shift the modeled burst peak, imposing unknown uncertainty. The best-fit d √ ξ b and (1 + z) factors of the baseline, Present § , Present ‡ , and Present † modeled light curves to the averagedobserved light curve and recurrence time of Epoch Jun 1998 are 7.38 kpc and 1.27, 7.46 kpc and 1.26, 7.34 kpc and 1.28, 7.50 kpc and 1.27, respectively. The averaged-modeled recurrence times of baseline, Present § , Present ‡ , and Present † are 5.11 h, 4.97 h, 5.13 h, and 5.03 h, respectively. The modeled recurrence times of the baseline and Present ‡ scenarios are in good agreement with the observed recurrence time, whereas the modeled recurrence times of the Present § and Present † scenarios are lower than the observed recurrence time by 0.17 h and 0.11 h, respectively, suggesting a 1 -2 % decrement can be applied for the accretion rate of the Present § and Present † models. Such decrement also indicates the new reaction rates used in the Present § and Present † models shorten up to 3 % of the recurrence time.

We define the burst-peak time, t = 0 s. The evolution time of light curve is respect to the burst-peak time. Figure 6 displays the best-fit modeled and observed XRB light curve profiles. The observed burst peak is located in the time regime t = −2.5 -2.5 s (top left inset in Fig. 6) , and at the vicinity of the modeled light-curve peaks of baseline, Present § , Present ‡ , and Present † . The overall averaged flux deviations between the observed epoch and each of these theoretical models, baseline, Present § , Present ‡ , and Present † in units of 10 −9 erg cm −2 s −1 are 1.175, 1.159, 1.149, and 1.252, respectively.

All modeled light curves are less enhanced than the observed light curve at t = 8 -125 s due to the reduction in accretion rate. The updated 59 Cu(p,γ) 60 Zn and 61 Ga(p,γ) 62 Ge reaction rates can induce enhancements at t = 8 -30 s and t = 35 -125 s, respectively (Lam et al. 2021b) , see also As(p,γ) 66 Se forward and reverse rates decrease the burst light curve at t = 40 -100 s (red line in Fig. 6 ), whereas the lower limit of the Present 65 As(p,γ) 66 Se forward and reverse rates produces a similar burst light curve profile as baseline (blue and black lines in Fig. 6 ). Note that the lower limit of the Present forward and reverse rates are based on a rather extreme S p ( 66 Se) uncertainty. The burst tail at t = 50 -80 s generated from the 65 As(p,γ) 66 Se forward and reverse rates using S p ( 66 Se) = 2.433 MeV, 2.443 MeV, and 2.507 MeV could be just 10 −9 erg cm −2 s −1 displaced from the burst tail of the Present † scenario (red line in Fig. 6 ) as long as the newly measured S p ( 66 Se) is within a range of ∼50 keV close to the present S p ( 66 Se) = 2.469 MeV. The baseline model that implements the NON-SMOKER 65 As(p,γ) 66 Se forward and reverse rates, can be a reference estimating the influence of the S p ( 66 Se) = 2.351 MeV, 2.381 MeV, and 2.284 MeV due to the rather close range of S p ( 66 Se). Besides, the 65 As(p,γ) 66 Se forward and reverse rates generated from the S p ( 66 Se) = 2.186 MeV may further enhance the burst tail end to be ∼1 × 10 −9 erg cm −2 s −1 higher than the baseline at t = 50 -80 s. The sensitivity study performed by Cyburt et al. (2016) on the influence of (p,γ) forward reaction rates does not exhibit that the 65 As(p,γ) 66 Se forward rate is influential, whereas the sensitivity study done by Schatz & Ong (2017) indicate that the 65 As(p,γ) 66 Se reverse rate possibly impacts the burst tail. Our present study with the newly deduced 65 As(p,γ) 66 Se forward and reverse rates shows that the correlated forward and reverse rates characterizes the burst tail.

The updated 22 Mg(α,p) 25 Al reaction maintains its role in increasing the burst light curve at t = 16 -60 s (yellow line in Fig. 6 ) even correlated influences among dominant reactions are included in the Present § model. This finding agrees with the preliminary result of Lam et al. (2021b) shown in the Supplemental Material of Hu et al. (2021) .

From t = 130 s onward, the baseline and Present §, ‡, † models successfully reproduce the tail end of the burst light curve of GS 1826−24. The modeled burst tail ends produced by Randhawa et al. (2020) are, however, over expanded which might be due to a somehow limited observed data that are selected for fitting the modeled burst light curves, see Fig. 4 in Randhawa et al. (2020) or in Hu et al. (2021) .

We perform a comprehensive study to understand the microphysics behind the differences among these modeled burst light curves with investigating the evolutions of accreted envelope regime where nuclei heavier than CNO isotopes are densely synthesized against the evolutions of the respective burst light curves of the 15 th , 16 th , 16 th , and 19 th burst for the baseline, Present § , Present ‡ , and Present † models, respectively. These selected bursts almost resemble the respective averaged light curve profile presented in Fig. 6 . The reference time of accreted envelope and nucleosynthesis in the following discussion is also relative to the burst-peak time, t = 0 s. The moment before and just before the onset. -The preceding burst leaves the accreted envelope with synthesized protonrich nuclei, which go through β + decays, and enrich the region around long half-live stable nuclei, e.g., 32 S, 36 Ar, 40 Ca, 60 Ni, 64 Zn, 68 Ge, 72 Se, 76 Kr, and 80 Sr, which are the remnants of waiting points. Meanwhile, the unburned hydrogen nuclei above the base of the accreted envelope keep the stable burning active until the freshly accreted stellar fuel stacks up, increasing the density of the accreted envelope due to the strong gravitational pull from the host neutron star of GS 1826−24 X-ray source for presetting the thermonuclear runaway conditions of the next XRB.

At time t = −10.2 s, just before the onset of the succeeding XRB, the temperature of the envelope reaches a maximum value of 0.9 GK for the baseline, and Present §, ‡, † scenarios, see Figs. 7, 8, and 17(a) . The 64 Ge abundance is around one to five orders of magnitude higher than other surrounding isotopes, whereas the ratio of 68 Se to 64 Ge abundances is ≈ 1.7. Meanwhile, the evolution of 64 Ge mass fraction in the mass coordinate of accreted envelope is qualitatively analogous to the 66 Se mass fraction. The 64 Ge abundance is comparable with the 60 Zn and 66 Se abundances (solid green, blue, and pink lines in Figs. 7, ..., 16) . These four factors indicate that 64 Ge is still a significant waiting point. The reaction flow passes through 68 Se and advances to heavier proton-rich nuclei region meanwhile the degenerate envelope is on the brink of the onset of XRB.

For the baseline scenario, the 2p-capture on 64 Ge waiting point is not yet developed, whereas for the Present ‡ scenario, the 2p-capture on 64 Ge is weak. The reaction flows of these two scenarios follow the weak GeAs II and sub-GeAs II cycles and mainly break out at 69 Se, see Fig. 1 for the reaction paths in the GeAs cycles. For the Present § and Present † scenarios, the 2p-capture on 64 Ge has already established, and the break-out flow at 69 Se is rather similar to the baseline and Present ‡ scenarios as the 68 Se and 69 Se abundances for these four scenarios are rather similar. The strong 2p-capture on 64 Ge in the Present § and Present † scenarios causes more than two orders of magnitude of 65 As and 66 Se cumulated in the GeAs cycles compared to the baseline and Present ‡ scenarios (dot-dashed cyan and dotted dark brown lines in top right insets of each panel in Figs. 7 and 8) . Using either the upper (or lower) limits of the new 64 Ge(p,γ) 65 As reaction rate (Lam et al. 2016 ) could mildly enhance (or reduce) the strength of 2p-capture on 64 Ge of drawing the synthesized materials from 64 Ge. Note that the GeAs cycles are still considered weak as compared to the NiCu and ZnGa cycles, nevertheless, the reaction flows in the GeAs cycles of the Present § and Present † scenarios is stronger than the ones in baseline and Present ‡ scenarios. The high 66 Se abundance in the Present § and Present † scenarios are due to the implementation of the Present 65 As(p,γ) 66 Se forward (and reverse) reaction rate, which is a factor of ∼1.7 higher than (a factor of ∼4.5 lower than) the NON-SMOKER 65 As(p,γ) 66 Se forward (reverse) rate at T = 0.9 GK used in baseline, and is about two orders (∼1.5 order) of magnitude higher than the lower limit of Present 65 As(p,γ) 66 Se forward (reverse) rate used in Present ‡ , see Fig. 4 .

The moment at t = −7.5 s before the burst peak. -Overall the light curves of the baseline, Present ‡ , Present § , and Present † scenarios rise to 15. 4, 16.3, 16.2, and 14.9 in units of 10 −9 erg cm −2 s −1 , respectively (top left insets of each panel in Figs. 9 and 10, and Fig. 17(b) ). The modeled light curve is quantitatively comparable with the observed bolometric flux. As the temperature of the envelope rises to around 1.1 GK, the 2p-capture on 64 Ge waiting point and the weak GeAs cycles starts establishing in the baseline and Present ‡ scenarios, which are about 2.5 s later than the Present § and Present † scenarios because both 65 As(p,γ) 66 Se rates used in the baseline and Present ‡ scenarios are up to (or more than) a factor of 2.5 in T = 0.4 -1.1 GK lower than the one used in the Present § and Present † scenarios (Fig. 4) . Also, the reverse 65 As(p,γ) 66 Se rate used in baseline is about a factor of 8.5 higher than the Present reverse rate used in Present §, ‡, † , causing a rather low cumulation of 66 Se in baseline.

The mass fractions of synthesized nuclei in the GeAs cycles evolve inversely with the rise of temperature of envelope along the mass zone, except 66 Se (and 65 As for the baseline scenario). The evolution of productions of 65 As, 66 Se, 66 As, 67 Se, 67 As, 68 Se, and 68 As up to this moment indicates that a strong reaction flow is formed along the 64 Ge(p,γ) 65 As (p,γ) 66 Se(β + ν) 66 As(p,γ) 67 Se(β + ν) 67 As(p,γ) 68 Se(β + ν) 68 As(p,γ) 69 Se path for these four scenarios. The grow of 65 As mass fraction in the baseline is due to the higher NON-SMOKER 65 As(p,γ) 66 Se reverse rate using the S p ( 66 Se) = 2.349 MeV, indicating that some material is temporarily stored as 65 As in the baseline scenario. For the Present §, ‡, † scenarios, more material is transmuted from 65 As and temporarily stored as 66 Se, which then decays via (β + ν) channel and quickly transmutes to 69 Se and surge through the heavier proton-rich region.

The moment at the vicinity of the burst peak. -The accreted envelopes of baseline, Present ‡ , Present § , and Present † reach the maximum temperature at times −0.9 s (1.33 GK), −1.1 s (1.34 GK), −1.5 s (1.34 GK), and −0.8 s (1.34 GK), respectively. The rise of temperature in the envelope before the burst peak for all scenarios due to the mutual feedback between the nuclear energy generation and hydrodynamics during the onset induces the release of material stored in dominant cycles of nuclei lighter than 64 Ge. Due to the lower 65 As(p,γ) 66 Se reaction rates used in baseline and Present ‡ , less material is drawn to 68 Se causing the production of 64 Ge surpasses 68 Se in these two scenarios. In fact, both 64 Ge and 68 Se have already been produced and cumulated when t ≈ −10.6 s or ≈ 0.5 s before the onset.

The location of the observed burst peak could be at ±0.5 s away from the modeled burst peaks of these four scenarios (top left insets of each panel in Figs. 11 and 12, and Fig. 17(c) ). Note that the advantage of impartially fitting the whole observed burst light curve helps us to avoid unexpectedly shifting the modeled burst peak further away from the thought location of observed burst peak. Such misalignment with the observed burst peak occurs in the modeled burst peaks produced by Randhawa et al. (2020) models, see Fig. 4 in Randhawa et al. (2020) or in Hu et al. (2021) .

We find that the Present § model uses the latest 22 Mg(α,p) 25 Al reaction rate (Hu et al. 2021 ) which extends the dominance of 22 Mg(p,γ) 23 Al reaction up to 1.67 GK. This causes the reaction flow in the Present § scenario mainly follows the 22 Mg(p,γ) 23 Al(p,γ) 24 Si path at the 22 Mg branch point that is faster for the reaction flow to synthesize more proton-rich nuclei nearer to proton dripline than the 22 Mg(α,p) 25 Al(p,γ) 26 Si path and gives rise to more hydrogen burning at later time.

The moment at t ≈ 30 s after the burst peak. -The consequence of more hydrogen burning caused by the latest 22 Mg(α,p) 25 Al reaction rate, which is almost one order of magnitude lower than the NON-SMOKER 22 Mg(α,p) 25 Al reaction rate, manifests on the enhancement of burst light curve at time regime t = 16 -60 s for the Present § scenario (top left insets of each panel in Figs. 13 and 14 , and Fig. 17(d) ). Such enhancement is consistent with that was found by Hu et al. (2021) , and exhibits the role of important reactions found by Cyburt et al. (2016) improving the modeled burst light curve.

The moment at t ≈ 65 s after the burst peak. -The modeled burst light curves diverge at t ≈ 45 s and reach a distinctive difference at t ≈ 65 s (top left insets of each panel in Figs. 15 and 16, and Fig. 17(e) ). Materials that have been released since around the burst-peak period from cycles in sd-shell, e.g., the NeNa, SiP, SCl, and ArK cycles, in bottom pf -shell, e.g., the CaSc cycle, have passed through the NiCu, ZnGa, and weak GeAs cycles, enrich the region beyond Ge and Se. The 2p-capture on 64 Ge for baseline and Present ‡ only lasts until t = 21.4 s and t = 35.8 s, respectively, whereas for Present § and Present † , this 2p-capture lasts until t = 49.1 s and t = 58.6 s, respectively. The longer time the 2p-capture on 64 Ge extends in the XRBs, the more material is transferred via the 64 Ge(p,γ) 65 As(p,γ) 66 Se(β + ν) 66 As(p,γ) 67 Se(β + ν) 67 As(p,α) 68 Se(β + ν) 68 As(p,α) 69 Se path to surge through the region above Se with intensive (p,γ)-(β + ν) reaction sequences depleting accreted hydrogen appreciably (solid black lines in the top right inset of each panel in Figs. 15 and 16) . The H exhaustion in the envelope quenches the (p,γ) reactions, reduces the syntheses of proton-rich nuclei, and the produced proton-rich nuclei are left to sequential (β + ν) decays increasing the production of daughter nuclei, e.g., 62 Zn, 66 Ge, 60 Ni, and 64 Zn, which are the daughter nuclei of the ZnGa and GeAs cycles, and 60 Zn and 64 Ge waiting points.

The baseline and Present §, ‡, † models that we construct reproduce the burst tail end of GS 1826−24 clocked burst from t = 130 s onward with excellent agreement with the averaged-observed Epoch Jun 1998. Nevertheless, the burst tail ends produced by Randhawa et al. (2020) both baseline and updated model are over expanded and misaligned with observation (Epoch Sept 2000) . Such deviation indicates that their modeled burst does not recess in accord with the observation and H-burning may somehow be still active in the envelope. The deviation could also be due to the limited data specifically chosen for fitting the modeled burst light curve or due to the astrophysical settings of both models, see Fig. 4 in Randhawa et al. (2020) or in Hu et al. (2021) . The onezone model constructed by Schatz & Ong (2017) successfully estimate a gross feature of the burst light curve influenced by a scaled 65 As(p,γ) 66 Se reaction rate (with S p ( 66 Se) of 100 keV uncertainty larger than the one used in NON-SMOKER 65 As(p,γ) 66 Se rate), however, the H-burning diminishes earlier than their baseline model due to the implemented extreme parameters (Schatz 2021) , causing a more rapid decrease of the burst tail end.

The compositions of burst ashes generated from the baseline and Present §, ‡, † models are presented in Fig. 18(f) . The temperature of accreted envelope decreases from 0.8 GK to 0.64 GK starting from t = 65 s to 150 s. The weak feature of the latest 22 Mg(α,p) 25 Al reaction rate, which is more than two order of magnitudes lower than the 22 Mg(p,γ) 23 Al reaction at T = 0.8 -0.64 GK, allows more nuclei to be produced via the 22 Mg(p,γ) 23 Al(p,γ) 24 Si reaction flow. The material in the reaction flow is then stored in the dominant cycles in sd-shell nuclei, e.g., the SiP, SCl, and ArK cycles. As H is then almost depleted, decreasing nuclear energy generation from (p,γ) reactions and causing the drop in temperature, the reaction flow is less capable to break out from cycles in pfshell nuclei. The synthesized materials are kept in these cy-cles until the end of the burst. Therefore, the implementation of the latest 22 Mg(α,p) 25 Al in the Present § model increases the production of hot CNO cycle and sd-shell nuclei up to a factor of 4.5 (for 12 C which could be the main fuel for Type-I X-ray superburst; Cumming et al. 2006) . Meanwhile, compared to the baseline model, the abundance of 12 C isotope is increased about a factor of 4.2 based on the Present ‡ model. These nuclei mainly are the remnants (daughter nuclei) left over from the proton-rich nuclei in the dominant cycles of pand sd-shell nuclei. Such enrichment of sd-shell nuclei enhances the light nuclei abundances that eventually sink to the neutron-star surface.

We notice that a periodic increment exhibits in the remnant of A = 64 -88 nuclei up to a factor of 1.4, with leading increment of waiting points remnants, A = 64, 68, 72, 76, 80, 84, and 88 . This indicates that a set of even weaker cycles resembling the weak GeAs II and sub-II cycles exists at waiting points heavier than 68 Se. Nonetheless, the 2pcapture on waiting point feature is extremely weak for waiting points heavier than 64 Ge, e.g., 68 Se, 72 Kr, 76 Sr, 80 Zr. The periodic increment of Present § is weaker than Present ‡ and Present † because materials are still stored in the dominant cycles of sd-shell nuclei due to the weak 22 Mg(α,p) 25 Al reaction. Moreover, the abundances of nuclei A > 100 decreases for the Present §, ‡, † models as more materials are kept in the cycles of sdand pf -shell nuclei.

Using the best-fit modeled burst light curve produced from the baseline and Present §, ‡, † models, we estimate (1 + z) = 1.26 +0.04 −0.05 , of which the uncertainty is based on the averaged deviation (2 %) of comparing the modeled light curves with the averaged-observed light curve of Epoch Jun 1998. The range of host neutron-star mass-radius relation, M NS -R NS , of the GS 1826−24 X-ray source is then estimated using our best-fit (1 + z) and Eq. (1) of Johnston et al. (2020) . The deduced range of M NS -R NS for GS 1826−24 is compared with recently assessed M NS -R NS constraints, i.e., the M NS of PSR J0348+0432 and PSR J1614−2230 deduced by Antoniadis et al. (2013) and Demorest et al. (2010) , respectively, based on Shapiro time delay (overlapping pink strips in Fig. 19) , the M NS -R NS of PSR J0740+6620 estimated recently by Riley et al. (2021) using Bayesian analysis (green zone in Fig. 19) , the M NS of PSR J1903+0327 and PSR J1909−3744 compiled by Arzoumanian et al. (2013;  distinctive light pink strips in Fig. 19 ), the R NS range of neutron stars with M NS = 1.4, 1.7, and 2M proposed by Steiner et al. (2018;  three yellow lines in Fig. 19) , the M NS -R NS of GS 1826−24 proposed by Johnston et al. (2020) using Markov chain Monte-Carlo method to estimate the properties of three epochs (dark purple line in Fig. 19 ), lower and upper limits of R NS given by Bauswein et al. (2017;  black dot in Fig. 19 ) and by Fattoyev et al. (2018; blue dot in Fig. 19 ) based on the study of GW170817 neutron-star merger.

The presently estimated range of M NS -R NS for GS 1826−24 (light red zone in Fig. 19 ) overlaps with the constraints suggested by Johnston et al. (2020) and Steiner et al. (2018) (Fig. 19) , presuming that its M NS -R NS is likely in the range of M NS 1.7M and R NS ∼12.4 -13.5 km. This suggests that the radius of PSR J1903+0327 could be close to the range of 12.4 R NS /km 13.5, and neutron stars with M NS ≈ 1.7M could be less compact than that were estimated by Guillot et al. (2013) .

We emphasize that as the present neutron-star mass-radius constraint is based on (1 + z) = 1.26 +0.04 −0.05 deduced from XRB models with averaged deviations between modeled and observed burst light curves up to 1.252 × 10 −9 erg cm −2 s −1 , a (1 + z) factor deduced from a well match modeled and observed burst light curve with much lower deviation is highly desired to provide a more reasonable constraint.

As(p,γ) 66 Se forward and reverse, 56 Ni(p,γ) 57 Cu(p,γ) 58 Zn, 55 Ni(p,γ) 56 Cu, and 64 Ge(p,γ) 65 As reactions. The affected burst-ash compositions consist of nuclei in hot CNO cycle, sd and pf shells, up to A = 140, except A = 87, . . . , 96. Both Present § and Present † models show that the abundances of nuclei A = 64, 68, 72, 76, and 80 are affected up to a factor of 1.4. The inclusion of the updated 22 Mg(α,p) 25 Al reaction rate in Present § influences the production of 12 C up to a factor of 4.5 that could be the main fuel for superburst. A set of noticeably periodic increment of burst-ash abundances exists in the region heavier than 64 Ge with waiting points leading the increment, indicating that the resemblance of 2pcapture and weak GeAs cycles also coexists in the region during the thermonuclear runaway.

We remark that the impartial fit on the whole timespan of burst light curve permits us to produce a set of modeled burst light curves with excellent agreement with the observed Epoch Jun 1998 at burst peak and tail end, and the distinguished feature of the light curve is reproduced. The averaged deviation of between modeled and observed burst light is only up to 1.252 × 10 −9 erg cm −2 s −1 . The best-fit modeled bursts, which diminish accordingly with observation and with considerably low discrepancy, presumably provides a set of more convincing burst-ash abundances that are not observed. This permits us to understand the nucleosyntheses that happen during the thermonuclear runaway in the accreted envelope. The modeled burst light curve produced by Randhawa et al. (2020) is, however, rather extensive and the H-burning does not recede accordingly with observation, and also the modeled burst peak is misaligned with observation. The one-zone model constructed by Schatz & Ong (2017) successfully obtains the influence of 65 As(p,γ) 66 Se reaction rate (with larger S p ( 66 Se) compared to the NON-SMOKER 65 As(p,γ) 66 Se rate) on a gross feature of burst light curve, however, the H-burning recedes earlier than their baseline model, accelerating the recession of burst tail end.

In this work, we presume the radius of the host neutron star of GS 1826−24 to be in the range of ∼ 12.4 -13.5 km as long as its mass 1.7M . Besides, the radius of PSR J1903+0327 could be likely close to the range of 12.4 R NS /km 13.5, and future observations could shed light on the estimation of neutron-star radii coupled with M NS ≈ 1.7M . This presumption indicates that the neutronstar compactness estimated by Guillot et al. (2013) is somehow more compact.

We are deeply grateful to H. Schatz for reading our manuscript and for providing thoughtful and constructive suggestions to improve the manuscript, and to B. A. Brown for providing the previous and updated S p ( 66 Se) and for reading and suggesting constructive thoughts to the part related to the S p ( 66 Se). We thank W. J. Huang for providing the information of AME. We also thank the anonymous referee for the helpful comments and remarks on this manuscript.

Se) values are obtained from folding the experimental 66 Ge and 65 Ge nuclear masses and theoretical MDEs, or the experimental 66 Ge and 65 As nuclear masses and theoretical MDEs. The S p ( 66 Se) = 2.469±0.054 MeV is selected to be the reference. The 54-keV uncertainty is deduced from the rms deviation of comparing both theoretical and updated experimental MDEs (AME2020). Then, using the full pf -model space shell-model calculations with the GXPF1a Hamiltonian, we choose S p ( 66 Se) = 2.469 MeV as a reference, and conservatively assume the uncertainty to be 100 keV to estimate the extent of the new 65 As(p,γ) 66 Se forward and reverse reaction rates to cover other estimated S p ( 66 Se), i.e., S p ( 66 Se) = 2.433 MeV, 2.443 MeV, and 2.507 MeV, whereas the forward and reverse reaction rates based on S p ( 66 Se) = 2.186 MeV, 2.351 MeV, and 2.284 MeV are calculated as well. We comprehensively study the influence of the new rate on the burst light curve of GS 1826−24 clocked burster, nucleosynthesis in and evolution of the accreted envelope, and burst-ash abundances at the burst tail end. Future precisely measured S p ( 66 Se) with uncertainty lower than or ≈ 50 keV can confirm our present findings and predictions

X-ray source, the more material is transferred via the

+ ν) 66 As(p,γ) 67 Se(β + ν) 67 As

Se path to reach the region heavier than Se of which intensive (p,γ)-(β + ν) reaction sequences ascertainably burn accreted hydrogen, release nuclear energy, and thus increase the burst light curve. Meanwhile, the status of 64 Ge as an important and historic waiting point is affirmed by analogizing the evolution of 64 Ge production with the synthesis of 66 Se along the mass coordinate of accreted envelope

We also include the new 22 Mg(α,p) 25 Al reaction rate in our study, and find that its influence on the clocked XRB at time regime t = 16 s -60 s and burst-ash compositions is stronger than other considered reactions

Thermonuclear Burning on Rapidly Accreting Neutron Stars

Burst Environment, Reactions and Numerical Modelling Workshop (BERN18)

Direct measurement of 22 Mg

The 16th International Symposium on Nuclei in Cosmos XVI (NIC-XVI)

The Nuclear Many-Body Problem

Cauldrons in the Cosmos

IJMSp

Proc. 23rd ESLAB Symposium on Two Topics in X-Ray Astronomy

IJMSp

We are very thankful to N. Shimizu for suggestions in tuning the KSHELL code at the PHYS T3 (Institute of Physics) and QDR4 clusters (Academia Sinica Grid-computing Centre) of Academia Sinica, Taiwan, to D. Kahl for checking and implementing the newly updated 56 Ni(p,γ) 57 Cu reaction rate, to M. Smith for using the Computational Infrastructure for Nuclear Astrophysics, and to J. J. He for fruitful discussion. This work was financially supported by the Strategic Priority Research Program of Chinese Academy of Sciences (CAS, Grant Nos. XDB34000000 and XDB34020204) and National Natural Science Foundation of China (No. 11775277). We are appreciative of the computing resource provided by the Institute of Physics (PHYS T3 cluster) and the Academia Sinica Grid-computing Center (ASGC) Distributed Cloud resources (QDR4 cluster) of Academia Sinica, Taiwan