Reliable photonuclear reaction rates in stellar conditions are essential for understanding the origin of the heavy stable neutrondeficient isotopes between SUP74SUPSe and SUP196SUPHg i.e. pnuclei. However many reaction rates of relevance still have to rely on the HauserFeshbach HF model due to the rarity of experimental progress. One such case is in the mass range of 160 for Dy Er Ho and Tm isotopes. In this work we attempt to constrain the HF model in the TALYS package by reproducing the available experimental data on SUP160SUPDyp SUP161SUPHo and SUP162SUPErp SUP163SUPTm in the A  160 mass region and examine the effects of level density gamma strength function and the optical model potential. The constrained model then allows us to calculate the reaction rates of SUP157159SUPHo p and SUP163165SUPTm p for the process nucleosynthesis in a carbondeflagration model for Type Ia supernovae. Our recommended rates differ from the JINA REACLIB by more than one order of magnitude in the temperature range 23 GK. This results in changes in the final abundance of pnuclei in the A  160 mass range by 5.5 to 3 from those with JINA which means that the uncertainty of  p reactions is not predominant for the synthesis of these nuclei.
['P-process', '1195', 'Astrophysics - Solar and Stellar Astrophysics', 'Nuclear Experiment', 'Nuclear Theory']
Photonuclear Reaction Rates of SUP157159SUPHo and SUP163165SUPTm and Their Impact in the process
{'No Header': 'Draft version September 19, 2024  \nTypeset using L A T E X twocolumn style in AASTeX63', 'Photo-nuclear reaction rates of 157 , 159 Ho and 163 , 165 Tm and their impact in the γ -process': 'Hao Cheng, 1 Bao-Hua Sun, 2 Li-Hua Zhu, 2 Motohiko Kusakabe, 2 Yudong Luo, 3, 4 Toshitaka Kajino, 2, 5, 6 Chang-Jian Wang, 2 Xing-Qun Yao, 2 Chuang-Ye He, 1 Fu-Long Liu, 1 and Bing Guo 1  \n1 China Institute of Atomic Energy, Beijing 102413, P. R. China  \n2 School of Physics, and International Research Center for Big-Bang Cosmology and Element Genesis, Beihang University, Beijing 100191, P. R. China  \n3 School of Physics, Peking University, Beijing 100871, China  \n4  \nKavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China  \n5 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  \n6 Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan  \n(Received Month date, 2020; Revised Month date, 2020; Accepted Month date, 2020)', 'ABSTRACT': 'Reliable photo-nuclear reaction rates at the stellar conditions are essential to understand the origin of the heavy stable neutron-deficient isotopes between 74 Se and 196 Hgp -nuclei, however, many reaction rates of relevance still have to rely on the Hauser-Feshbach model due to rare experimental progress. One such case is in the mass range of 160 for Dy, Er, Ho and Tm isotopes. In this work we attempt to constrain the Hauser-Feshbach model in the TALYS package by reproducing the available experimental data of 160 Dy( p, γ ) 161 Ho and 162 Er( p, γ ) 163 Tm in the A ∼ 160 mass region, and examine the effects of level density, gamma strength function and the optical model potential. The constrained model then allows us to calculate the reaction rates of 157 , 159 Ho( γ , p ) and 163 , 165 Tm( γ , p ) for the γ -process nucleosynthesis in carbon-deflagration SNe Ia model. Our recommended rates differ from the JINA REACLIB by more than 1 order of magnitude in the temperature range of 2-3 GK. This results in the changes of final abundance of p -nuclei in the A ∼ 160 mass range by -5.5-3% from those with JINA, which means that the ( γ , p ) reactions uncertainty is not predominant for the synthesis of these nuclei.  \nKeywords: γ process, reaction rate, Hauser-Feshbach statistical model', '1. INTRODUCTION': "35 neutron-deficient stable nuclei between 74 Se and 196 Hg, called p -nuclei, cannot be synthesized via the s and r neutron-capture processes. One of the most favored production mechanisms for those nuclei is photodisintegration, the so-called γ -process (Woosley & Howard 1978; Rayet et al. 1990;  \nCorresponding author: Bao-Hua Sun  \nbhsun@buaa.edu.cn  \nCorresponding author: Li-Hua Zhu  \nzhulh@buaa.edu.cn  \nCorresponding author: Yudong Luo  \nyudong.luo@pku.edu.cn  \nHoward et al. 1991; Rayet et al. 1995; Fujimoto et al. 2003; Roberti et al. 2023). Core-Collapse Supernovae (CCSNe) and the thermonuclear supernovae (SNe Ia) are two main astrophysical sites where one believes that the γ -process could occur (Travaglio et al. 2011, 2014, 2018).  \nThe γ -process in CCSNe can produce p -nuclei in various mass ranges, and a recent study indicates that different progenitor models of CCSNe may provide different isotopic ratios of p -nuclei compared with the solar abundances (Roberti et al. 2023). Most p -nuclei in the mass ranges 124 ≤ A ≤ 150 and 168 ≤ A ≤ 200 can be produced in CCSNe, while there are severe deficiencies in the A ≤ 124 and A ∼ 160 mass regions, where the solar abundances are severely under-produced (Rauscher 2001; Rapp et al. 2006; Hayakawa et al. 2008; Rauscher et al.  \n2013; Pignatari et al. 2013). The γ -process could also occur in the explosions of carbon-oxygen white dwarf (WD) triggered by deflagration or detonation after accreting mass from a companion star (Howard et al. 1991; Kusakabe et al. 2005; Arnould & Goriely 2006; Kusakabe et al. 2011; Travaglio et al. 2011, 2014). The extensive s -process in the progenitor asymptotic giant branch (AGB) star (Battino et al. 2020) and the helium shell flashes during the mass accretion could produce seeds nuclei for γ -process. However, even for a presumption of a factor of 10 3 -10 4 overproduction of s -process seeds nuclei, the solar abundance pattern of p -nuclei could not be reproduced completely (Kusakabe et al. 2005, 2011; Rauscher et al. 2013). The abundances of nuclei in the mass range A ∼ 160 (i.e., 152 Gd, 156 , 158 Dy and 162 , 164 Er) are particularly noteworthy since they cannot be accounted for within the γ -process nucleosynthesis models in both scenarios we mentioned above (Rauscher et al. 2013).  \nBesides the two main scenarios, other astrophysical sites have also been discussed to potentially produce p -isotopes. For example, the isotropic fractions of 92 , 94 Mo and 96 , 98 Ru are 1-2 orders of magnitude larger than the other p -nuclei and their main production process has been suggested to νp -process (Frohlich et al. 2006; Wanajo et al. 2011; Sasaki et al. 2022). A newly proposed νr -process could be responsible for the production of p -nuclei (Xiong et al. 2024). Recent studies also suggest that 152 Gd and 164 Er are mainly reproduced by the s -process (Bisterzo et al. 2014; Travaglio et al. 2011).  \nThe p -nuclei production is sensitive to their seed s -and (or) r -process nuclei, whose abundances strongly depend on the stellar evolution before the supernova explosion. Therefore, the precise prediction of the p -nuclei abundances requires many important factors among the uncertainties of both astrophysical model and the nuclear input parameters. However, they have not yet been clearly determined. Modeling the synthesis of the p -nuclei and calculating their abundances (Song et al. 2022) in the γ -process require an extended reaction network calculation involving about 10 000 reactions on around 2000 stable and unstable nuclei (Arnould et al. 2003). The availability and uncertainties in nuclear data have a significant impact on the reaction rates and on the final abundance distribution of elements. Despite the concerted experimental efforts (Scholz et al. 2020; Fallis et al. 2020; Lotay et al. 2021; Cheng et al. 2021; Vasileiou et al. 2022; Wilden et al. 2023; Williams et al. 2023; Tsantiri et al. 2023), most of the nuclei involved are currently unavailable in the laboratory as they often involve unstable nuclei or extremely low isotopic frac-  \nions. Thus, reaction rates are frequently predicted relying on statistical Hauser-Feshbach (HF) theory models (Hauser & Feshbach 1952; Rauscher et al. 1997). Several popular software packages, such as TALYS (Koning et al. 2023), including various modifications of phenomenological and microscopic nuclear structure and reaction models, are extensively used nowadays for nuclear reaction calculations of different projectiles (Utsunomiya et al. 2003; Dillmann et al. 2011; Mei et al. 2015; Gyurky et al. 2006; Netterdon et al. 2014; Guray et al. 2009; Wu et al. 2020). However, the physical inputs inherent to the HF theory calculations may not have undergone well constrained verification. Ensuring the provision of reliable reaction rates necessitates conducting a validity test of the statistical HF model in the mass region of interest.  \nFor the case of the γ -process, the dominant reactions are photodisintegration reactions (( γ , n ), ( γ , p ) and ( γ , α )). However, despite the challenges in obtaining quasi-monoenergetic γ -rays, in most cases cross sections of ( p, γ ) and ( α, γ ) reactions have been measured to deduce their inverse, ( γ, p ) and ( γ, α ), which are related through the detailed balance theorem. For experimental studies related to p -nuclei in the A ∼ 160 mass region, very few proton capture measurements have been performed except for 162 Er ( Ozkan et al. 2017) and 160 Dy (Cheng et al. 2021). Experimental data of 156 Dy, 158 Dy, and 164 Er in this mass region are still unavailable due to the low cross section (0.3 nb ∼ 0.4 mb) at the energies of Gamow window and the low isotopic fractions (0.06% ∼ 1.60%). As an alternative, it's possible to utilize the known experimental data within a similar mass range to constrain the HF theoretical reaction models. The available cross section data in the A ∼ 160 mass region are 160 Dy( p , γ ) and 162 Er( p , γ ), obtained at proton laboratory energies ranging from 3.5 to 9.0 MeV, covering the majority of the Gamow window for each reaction. Subsequently, a short-range extrapolation is conducted to directly predict the photo-proton reaction rates of 157 , 159 Ho and 165 , 163 Tm, and to study their impact on the γ -process nucleosynthesis.  \nThe strong constraints on reaction models help to improve and guarantee the reliable results of the γ -process calculations. In the present paper, the experimental data for proton capture reactions on 160 Dy and 162 Er are compared with the TALYS-2.0 calculations obtained with various nuclear level density (NLD), optical model potential (OMP), gamma strength function (GSF), compound nucleus (CPN), and pre-equilibrium (pre-E). In Sec. 2, we present a comprehensive illustration of constraining the HF theory models using the experimental data, and identify the most influential nuclear mod-  \nls. We also compare the extracted reaction rates of 157 , 159 Ho( γ, p ) 156 , 158 Dy and 163 , 165 Tm( γ, p ) 162 , 164 Er with those from the JINA reaction library (Cyburt et al. 2010). In Sec. 3, we apply the new reaction rates to the nucleosynthesis in low-temperature layer of a carbondeflagration model for SNe Ia, which is not included in the previous study Kusakabe et al. (2011). We compare the p -nuclei final abundances between the derived rates and JINA REACLIB-V2.0 rates and discuss the overproduction factors of p -nuclei. Finally, we present the conclusions in Sec. 4.", '2.1. Theoretical Model Framework': "Necessary conditions for applying the statistical HF model, such as high excitation energies involving many overlapping energy states, are readily satisfied for many nuclear reactions in the γ -process. All existing γ -process calculations actually rely on a statistical HF model. For a reaction A i ( a, b ) B f , where the target nucleus A in initial level i captures an incident a , forming a compound nucleus which subsequently decays to final level f of residual B with emission of particle b , with a center of mass energy E Aa and reduced mass µ Aa for the entrance channel, the cross section σ i,f is given by:  \nσ i,f ( E Aa ) = π /planckover2pi1 2 / (2 µ Aa E Aa ) (2 J i A +1)(2 J a +1) ∑ J, Π (2 J +1) × T i a ( E,J, Π , E i A , J i A , Π i A ) T f b ( E,J, Π , E f B , J f B , Π f B ) T tot ( E,J, Π) , (1)  \nwhere J is the spin, E is the corresponding excitation energy, and Π represents the parity of excited states of residual B . T i a represents the transmission coefficient for formation of compound nucleus from entrance state i of a , and T f b is the transmission coefficient for evaporation of a particle b to the final state f of residual B from compound nucleus. The total transmission coefficient T tot = ∑ f,b T f b describes the transmission into all possible bound and unbound states f in all energetically accessible exit channels b (including the entrance channel A ). And T f b can be replaced by transmission coefficient into exit channel b :  \nT b ( E,J, Π) = f B ∑ f =0 T f b ( E,J, Π , E f B , J f B Π f B ) + ∫ E max B E f B B ∑ J B . Π B T b ( E,J, Π , E B , J B , Π B ) × ρ ( E B , J B , Π B ) dE B , (2)  \nwhere E f B B is the energy of the highest experimentally known bound excited state f B . ρ ( E B , J B , π B ) is the  \nNLD which describes the number of states with spin J B and parity π B at excitation energy E B .  \nThus, the important quantities for calculating a cross section from Eqs.(1) and (2) are the transmission coefficients of particles and γ -rays, and the NLD. The particle transmission coefficients are calculated using an OMP, and the γ -transmission coefficients are governed by GSF parameters. TALYS provides a variety of options for describing these inputs and is used hereafter to conduct the sensitivity studies.  \nThe sensitivity of the 160 Dy( p , γ ) and 162 Er( p , γ ) cross sections to charged-particle widths, neutron widths, and γ widths varies with respect to the center-of-mass energy, as depicted in Fig.1. The sensitivity s denotes the relative change of the cross section when one width is varied (Rauscher 2012):  \ns = σ ' σ -1 f -1 (3)  \nIn this context, σ ' σ represents the relative variation of the laboratory cross section and f = Γ ' Γ signifies the factor that adjusts the respective width. The neutron threshold for 160 Dy and 162 Er are 4.1 and 5.6 MeV, respectively. The nuclear-physics input parameters include NLD and GSF which determine the γ width. Moreover, the OMP are needed to describe the particle widths for protons and neutrons. 160 Dy( p , γ ) and 162 Er( p , γ ) cross sections are dominantly sensitive to the proton ( p ) width within the Gamow window. Above the neutron threshold, the effect of gamma ( γ ) and neutron ( n ) width increases with increasing energies.", '2.2. Constraining the Hauser-Feshbach Model': 'For the key ingredients (NLD, OMP, GSF, etc) in Hauser-Feshbach calculations, TALYS offers a variety of options for the description of these inputs. However, these options presented in TALYS are not a systematic variation of nuclear properties and therefore cannot be used as measure of uncertainty in the cross section prediction. It is beneficial to develop a sub-model combination for the mass region that can be applied to nearby nucleus where there is still limited or no available experimental data. Multiple (sub-)models are required to calculate crucial input variables such as NLD, GSF, OMP, nuclear masses, pre-equilibrium, and the compound process to perform accurate nuclear reaction calculations. We aim to find the optimal physical inputs for TALYS, which can accurately describe the known experimental data in A ∼ 160 mass region.  \nFor the available cross section in the mass region around A = 160, we found that TALYS calculations with default inputs for 160 Dy( p, γ ) 161 Ho are in  \nFigure 1. (Color online) Sensitivity s of the 160 Dy( p, γ ) 161 Ho (a) and 162 Er( p, γ ) 163 Tm(b) corss sections, when the p , n , α , and γ widths are varied by a factor of two, as a function of center-of-mass energies. The data are from Rauscher (2012). The shaded area denotes the Gamow window. Within the Gamow windows, the cross sections are predominantly sensitive to the p width.  \n<!-- image -->  \ngood agreement with the experimental data at 3-9 MeV (Cheng et al. 2021), as shown in Fig. 2(a). The TALYS result with the default parameters for the 162 Er( p, γ ) 163 Tm ( Ozkan et al. 2017) reaction is a factor of two smaller than the experimental data at 6.5-9 MeV, as shown in Fig. 2(b). The experimental data and TALYS calculations with default inputs are shown in Table 1. These calculations are expected to be a good starting point in extrapolations to the experimentally unknown mass region. In order to identify the model combinations that can reproduce these experimental data, different physical models implemented in the TALYS 2.0 code are sampled and varied to generate random input files with unique model combinations.  \nFigure 2. (Color online) TALYS calculation results compared with experimental data (black dots), for (a) 160 Dy( p, γ ) 161 Ho using default parameters (green line), one set of sampling models (color filled areas), and the optimized one (red line) best reproducing experimental data both of 160 Dy( p, γ ) 161 Ho and 162 Er( p, γ ) 163 Tm reactions; (b) 162 Er( p, γ ) 163 Tm using default parameters (green line), sampling models (blue filled area) and the optimized one (red line).  \nWe perform calculations in TALYS by varying 52 key physical inputs, as described by Koning et al. (2019). In total, 10 000 samples are calculated. The results create a large spread in distributions as shown in Fig. 2. In calculations, the experimental mass values are used. The results are well converged at low energies below neutron threshold, but deviates as the energy increases.  \nThe quality of the description of experimental data with different model combinations is estimated using the reduced chi-square calculation:  \nR 2 = 1 N -1 N ∑ i =1 ( σ exp -σ cal ) 2 (∆ σ exp ) 2 , (4)  \nwhere σ exp and σ cal are the experimental and calculated cross sections, and ∆ σ exp is the uncertainty of experimental data. N is the number of experimental data points. The least R 2 is 9.3. The reaction cross-section is most sensitive to the variations of the OMP, NLD, and GSF. Altering the OMP, NLD, and GSF result in changes in chi-square values by factors of up to 4, 17 and 11, respectively (see Table 2 for the relevant inputs).', '2.3. Constraining the models': "For the NLD, the Back-shifted Fermi gas model is used. The internal parameters constrained are the asymptotic level-density parameter ˜ a , the level-density damping parameter γ of the three nuclei in the protonentrance, neutron-exit, and γ -exit channels of each reaction. For example, in the proton induced reaction on 160 Dy, the final products, 160 Dy, 160 Ho and 161 Ho, are considered.  \nFor the GSF, E 1 transitions are calculated using the microscopic Hartree-Fock BCS tables. Regarding the OMP, the Koning and Delaroche OMP is used, which is suitable for protons and neutrons with incident energies from 1 keV up to 200 MeV, for (near-)spherical nuclides in the mass range 24 ≤ A ≤ 209 (Koning & Delaroche 2003). The parameters within these models are not varied and kept as the TALYS default. Below the neutron threshold, all the parameters are well constrained by the experimental data and tend to be similar as shown in Fig. 2. This also verifies the OMP can well describe the current reactions.  \nWe compare the cross sections to TALYS predictions using different asymptotic ˜ a and damping gamma, while keeping all other ingredients to the calculations fixed. For 160 Dy, 160 Ho, 161 Ho, the constrained ˜ a values are 17.14, 17.14, 17.23, respectively. All of the damping parameters are 0.072. The cross sections are mostly sensitive to the damping parameter γ for Back-shifted Fermi gas level density model. The cross sections of 160 Dy( p, γ ) 161 Ho and 162 Er( p, γ ) 163 Tm calculated by the constrained model and parameters ('TALYS optimized') are shown in Fig 2. TALYS optimized can be employed to evaluate the cross sections of the A ∼ 160 mass region.", '2.4. Evaluation of the Stellar Rate': "For reaction rates calculations, the ground state and the excited states of the target nucleus is assumed to be in thermodynamic equilibrium within the hot astrophysical plasmas. The various nuclear levels with spins and excitation energies are assumed to obey a MaxwellBoltzmann distribution. The 'TALYS optimized' calculation is found to well describe the experimental  \nFigure 3. (Color online) (a) Ratios of 157 Ho( γ, p ) 156 Dy and 159 Ho( γ, p ) 158 Dy stellar rates deduced from the 'TALYS optimized' and JINA (solid lines). The associated uncertainties are shown as the coloured bands. (b) The same as upper panel (a) but for the 163 Tm( γ, p ) 162 Er and 165 Tm( γ, p ) 164 Er reactions.  \n<!-- image -->  \n9  \ndata and is used to determine the reaction rates of 157 Ho( γ, p ) 156 Dy, 159 Ho( γ, p ) 158 Dy, 163 Tm( γ, p ) 162 Er and 165 Tm( γ, p ) 164 Er. The reaction rates in the temperature region of 0.1-10 GK are presented in Table 3. Table 4 shows coefficients of JINA analytical function for these photo-nuclear reaction rates at T 9 = [0 . 1 , 10], where T 9 is the temperature in units of 10 9 K. The function is given by:  \nN A 〈 σν 〉 ∗ = e ( a 0 + a 1 T -1 9 + a 2 T -1 / 3 9 + a 3 T 1 / 3 9 + a 4 T 9 + a 5 T 5 / 3 9 + a 6 lnT 9 ) , (5)  \nwhere a 0 -a 6 are the seven coefficients. For each reaction, Table 4 shows reaction rates fitting coefficients calculated using the 'TALYS optimized' model applicable to the A ∼ 160 nuclear region (the first row). The lower and upper bounds corresponding to a 20 % change in the R 2 value (second and third rows).  \nThe ratios between the present rates and the JINA recommended rates (Rauscher & Thielemann 2000) are shown in Fig. 3. Uncertainties of the present rates estimated based on the 'Random' are drawn with coloured bands. For 157 Ho( γ, p ) 156 Dy in Fig. 3 (a), the JINA underproduced the rates at T 9 =[0.4, 0.6] and [2.5, 5]. The JINA also underproduced the rates at T 9 = [0.3, 6] for 159 Ho( γ, p ) 158 Dy. For T = 2-3 GK relevant to the γ -process, the ratios for the 157 Ho( γ , p ) 156 Dy and 159 Ho( γ , p ) 158 Dy reactions are 0.3 -2.0 and 0.1-0.4, respectively. Fig. 3 (b) shows that our rates of 163 Tm( γ, p ) 162 Er and 165 Tm( γ, p ) 164 Er are larger by factors of 0.5-20.8 and 0.6-25.7 at T 9 = 2 -3, respectively.", '3. γ -PROCESS RESULTS': "In this section, we evaluate the relevant changes in the nuclear final abundances of the γ -process corresponding to the evaluated uncertainties. A previous study on the carbon-deflagration model of SNe Ia (Kusakabe et al. 2011) indicates that several isotopes, such as 138 La, 152 Gd, 156 , 158 Dy, 162 , 164 Er, 168 Yb, 174 Hf, 180 Ta, 184 Os and 196 Hg, could be more produced in a low temperature and density region. Such an enhancement could help to reproduce the solar p -nuclei abundances. Therefore, we set trajectories with peak temperatures T 9p = [2 , 2 . 9] and peak density ρ p = 10 6 g cm -3 for the γ -process layer in SNe Ia. Such astrophysical condition is also critical for the γ -process nucleosynthesis at the base of oxygen convective shell or in a C-O shell merger as pointed out in Rauscher (2001). We use the analytical profile of temperature and density as T 9 = T 9p exp[ -t/ (3 τ )] and ρ = ρ p exp( -t/τ ) with τ = 1 s. The initial nuclear composition is Case A1 in Kusakabe et al. (2011). The γ -process is then calculated as in Cheng et al. (2021) that includes updated rates of 16 O( n , γ ) 17 O (He et al. 2020) and 17 O( n , γ ) 18 O (Zhang et al. 2022).  \nAbundances of nuclei around 156 , 158 Dy in the case with the 'optimized' fitted rates of 157 , 159 Ho( γ , p ) for the profile of T 9p = 2 . 5 are shown in upper panel of Fig. 4. Nuclei are produced at an early time of t /greaterorsimilar 0 . 001 s and then destroyed both via photodisintegration reactions. In addition, their fractional changes from the case of JINA rates, i.e., ( Y i -Y i JINA ) /Y i JINA , are shown in lower panel of Fig. 4. The adopted rates for the reactions 157 , 159 Ho( γ , p ) 156 , 158 Dy are lower than the JINA rates, and the fractional changes in the 156 , 158 Dy abundances are negative and those in the 157 , 159 Ho abundances are positive.  \nUpper panel of Fig. 5 shows the abundances of nuclei around 162 , 164 Er in the case with the best fit rates of 163 , 165 Tm( γ , p ) for the profile of T 9p = 2 . 5. The effect of photodisintegration occurs at an early time. Abundance  \nFigure 4. (Color online) Abundances of nuclei around 156 , 158 Dy (upper panel) in the case with the 'optimized' fit rates in this paper and their fractional changes from the case of JINA rates, i.e., ( Y i -Y i JINA ) /Y i JINA (lower panel) for the profile of T 9p = 2 . 5.  \n<!-- image -->  \nincreases at t /greaterorsimilar 0 . 1 s when the neutron capture becomes more rapid than photodisintegration. In addition, their fractional changes from the case of JINA rates are shown in lower panel of Fig. 5. The adopted rates for the reactions 163 , 165 Tm( γ , p ) 162 , 164 Er are higher than the JINA rates. The 162 Er abundance in the best fit case is higher than those in cases of the JINA rates, and the 164 Er abundance is higher at first but becomes smaller. The 163 Tm abundance is lower, and the 165 Tm abundance is lower but its fractional change increases later. The 164 Er abundance is higher at first but then becomes smaller. At a later epoch, 164 Er as well as 165 Tm increase.  \nAbundance increases at later time are caused by production via the β + -decay and electron capture of nuclei on the proton-rich side. Then, fractional changes tend to approach to zero due to production via the decay and  \nFigure 5. (Color online) The same as in Fig.4 but for nuclei around 162 , 164 Er.  \n<!-- image -->  \nelectron capture at a later time when the photodisintegration is not operative.  \nThe final abundances and their fractional changes from the case of JINA rates in nuclear mole fractions are shown in upper and lower panels of Fig. 6, respectively, as a function of the peak temperature T 9p for 152 Gd, 156 , 158 Dy, and 162 , 164 Er. Thick lines correspond to the best fit rates in this paper, and thin lines correspond to upper and lower limits for two cases. The upper and lower limits are estimated from variations in abundances caused by the four ( γ , p ) reactions for the 20 % χ 2 case. Changes in the final abundances between the cases with our best-fit rates and JINA rates are within -5.5-3 %.  \nIn Fig. 7 we compare the normalized overproduction factors of p -nuclei with A > 130. The final averaged overproduction factor 〈 F 〉 /F 0 is calculated for each isotope, where F 0 = ∑ j 〈 F 〉 j / 35 is the average value for 35 p -nuclei. 〈 F 〉 = ∑ i F i /N , where F i = Y i /Y /circledot is the overproduction factor in a trajectory i , and N is the total trajectory number. Y /circledot is the solar abundance value  \nFigure 6. (Color online) Final abundances (upper panel) and their fractional changes from the case of JINA rates (lower panel) in nuclear mole fractions as a function of the peak temperature T 9p for five p -nuclei. The values are taken at a longer simulation time, i.e. , 1 year after the peak temperature. Thick lines correspond to the best fit rates in this paper, and thin lines correspond to upper and lower limits on the ranges of 20 % χ 2 .  \n<!-- image -->  \ntaken from Anders & Grevesse (1989). Kusakabe et al. (2011) calculated more realistic overproduction factors by including the ejection mass of different layers in W7 Model, however, their calculation did not cover the temperature range in this work. Therefore, we added our result to the 〈 F 〉 value in their paper to include the contribution from other ejecta of W7 Model.  \nAs shown in Fig. 7, the production of 138 La and 180 Ta are enhanced as expected. This might raise an importance of γ -process contribution to the solar system abundance of these nuclei whose main production process is claimed to be SNII ν -process (Woosley et al. 1990; Hayakawa et al. 2010; Kajino et al. 2014), although the calculated results depend on modeling profile  \nFigure 7. Average overproduction factors calculated by our rates (open circles) compared with JINA (triangles) and Kusakabe et al. (2011) (diamonds). The horizontal solid and dashed lines correspond to 〈 F 〉 /F 0 equals to 1 and (3 , 1 / 3), respectively.  \n<!-- image -->  \nof the peak temperature. Moreover, not all p -nuclei with N > 82 can be enhanced in such a temperature layer, although there are slight increase in 152 Gd, 158 Dy, 184 Os abundances in our calculations (open circles) from JINA (triangles) in Fig. 7. Also, 152 Gd, 156 , 158 Dy, 162 , 164 Er under-production could not be resolved, even from an accurate determination of the ( γ, p ) reaction rates. The circles and triangles overlapped, because the main nucleosynthetic chain under this layer is the ( γ, n ) reactions. Therefore, taking into account the lower temperature layer in the carbon-deflagration model for SNe Ia, γ -process could not reproduce all the p -nuclei abundances. The uncertainty of ( γ, p ) reactions rates only contribute ≤ 5% of the final abundances for the nuclei in the mass range A ∼ 160. Therefore, the underproduction of these nuclei is not explained by a single carbon-deflagration SNe Ia event near the solar system with a near-solar abundance of s-nuclei.", '4. CONCLUSION': "For accurate γ -process calculations and potential enhancements in theoretical predictions of p -nuclei abundances, particularly within the A ∼ 160 mass region, we have determined the optimized TALYS physical inputs  \nfor this mass range. We utilized the available experimental data to constrain the GSF and NLD, which are critical inputs in the HF statistical model. Additionally, other significant inputs in TALYS, namely, compound models, pre-equilibrium models, and optical models, were also subjected constraints. We derive stellar rates using the 'TALYS optimized' model sets for 157 Ho( γ, p ) 156 Dy, 159 Ho( γ, p ) 158 Dy, 163 Tm( γ, p ) 162 Dy and 165 Tm( γ, p ) 164 Er in the range of T 9 =[0.1, 10] for γ process calculations. Compared to stellar rates provided by JINA database, our results for the best-fit cases of TALYS are different by up to one to two orders of magnitude. We applied carbon-deflagration SNe Ia γ -process for trajectories with a peak temperature 2 -2 . 8 GK. Our new rates in the four reactions can cause changes in five p -nuclei, that is, 152 Gd, 156 , 158 Dy, and 162 , 164 Er, with -5 . 5 ∼ 3% differences in the final abundances at the most sensitive temperature (2 . 4 -2 . 5 GK). This indicates that if the ( γ, p ) rates for many seed nuclei on the n -deficient region are revised substantially, final abundance of p -nuclei are possibly to be revised within such a ratio. However, if we averaged the production in the final trajectories, the shifts in final abundances would be ≤ 5%. Actually our calculated result showed that the nuclei near mass number A ∼ 160 could not be significantly synthesized to reproduce the solar abundance observation. Therefore, the solar abundance of those p -nuclei might not be explained as a single carbondeflagration SNe Ia event.", 'ACKNOWLEDGMENTS': 'We thank two anonymous referees for their valuable suggestions and extend our gratitude to Prof. Yuan Tian for helpful discussions on the reaction rates. This work was supported partially by the National Key R&D Program of China (Contract No.2022YFA1602401), the National Natural Science Foundation of China (Nos.12305149, 12325506, 11961141004, 12205378, 12335009, 11575018, 12125509, 11961141003), Young Talents Fund of China National Nuclear Corporation under Grant (Nos. FY010260623371, FY212406000901).', 'REFERENCES': "Arnould, M., Goriely, S, &Takahashi, K. 2003, PhR, 384, 1.  \nArnould, M., & Goriely, S. 2006, NuPhA, 777, 157. Anders, E. & Grevesse, N. 1989, GeoCoA, 53, 197. Wanajo, S., Janka, H.-T., & Kubono, S. 2011, ApJ, 729, 46.  \nBattino, U., Pignatari, M., Travaglio, C., et al. 2020,  \nBisterzo, S., Travaglio, C., Gallino, R., et al. 2014, ApJ,  \nMNRAS, 497, 4981. 787, 10.  \n- Cyburt, R. H., Amthor, A. M., Ferguson, R., et al. 2010, ApJS, 189, 240.\n- Cheng, H., Sun, B. H., Zhu, L. H., Li, T. X. , & Li, et al. 2020, Nuclear Science and Techniques, 31, 99.  \nCheng, H., Sun, B.H., Zhu, L.-H., et al. 2021, ApJ, 915, 78. Dillmann, I., Coquard, L., Domingo-Pardo, C., et al. 2011, PhRvC, 84, 015802.  \nFallis, J., Akers, C., Laird, A. M., et al. 2020, Physics Letters B, 807, 135575.  \nFujimoto, S.-. ichirou ., Hashimoto, M.-. aki ., Koike, O., et al. 2003, ApJ, 585, 418.  \n- Frohlich, C., Mart'ınez-Pinedo, G., Liebendorfer, M., et al. 2006, PhRvL, 96, 142502.\n- Gyurky, G. , Fulop, Z. , Somorjai, E. , Kokkoris, M. , & Goriely, S. 2003, PhRvC, 68, 1193.\n- Gyurky, G., Kiss, G. G., Elekes, Z., et al. 2006, PhRvC, 74, 025805.\n- Guray, R. T., Ozkan, N., Yal¸cın, C., et al. 2009, PhRvC, 80, 035804.\n- Guray, R. T, Ozkan, N, Yal¸cın, C, Rauscher, T. , & et al. 2015, PhRvC, 91, 055809.\n- Hauser, W. , & Feshbach, H. 1952, PhR, 87, 366.\n- Hayakawa, T., Iwamoto, N., Kajino, T., et al. 2008, ApJ, 685, 1089.\n- Hayakawa, T., Kajino, T., Chiba, S., et al. 2010, PhRvC, 81, 052801.\n- He, L. C., Diao, L. J. , Sun, B. H. , & Zhu, L. H. 2018, NIMPA, 880, 22.\n- He, M., Zhang, S. S., Kusakabe, M., Xu, S. Z., et al. 2020, ApJ, 899, 133.\n- Hilaire, S. , & Goriely, S. 2008, AIPC, 1012, 356.\n- Howard, W. M., Meyer, B. S., & Woosley, S. E. 1991, ApJL, 373, L5.  \nIwamoto, N., Umeda, H., & Nomoto, K. 2005, in Origin of Matter and Evolution of Galaxies 2003, ed. M. Terasawa et al. (Hackensack: World Scientific), 493.  \n- Kajino, T., Mathews, G. J., & Hayakawa, T. 2014, Journal of Physics G Nuclear Physics, 41, 044007.  \nKusakabe, M., Iwamoto, N., & Nomoto, K. 2005, NuPhA, 758, 459.  \n- Kusakabe, M., Cheoun, M.K., Kim, K. S., et al. 2006, ApJ, 872, 164.\n- Kusakabe, M., Iwamoto, N., & Nomoto, K. 2011, ApJ, 726, 25.\n- Koning, A. J. & Delaroche, J. P. 2003, NuPhA, 713, 231.\n- Koning, A. J., Rochman, D., Sublet, J.-C., et al. 2019, Nuclear Data Sheets, 155, 1.\n- Koning, A., Hilaire, S., & Goriely, S. 2023, European Physical Journal A, 59, 131.  \nWoosley, S. E., Hartmann, D. H., Hoffman, R. D., et al. 1990, ApJ, 356, 272.  \nWoosley, S. E, & Howard, W. M 1978, ApJS, 36, 285. Wu, D., Wang, N.Y., Guo, B., et al. 2020, PhLB, 805, 135431.  \nWilden, S., Heim, F., Muller, M., et al. 2023, European Physical Journal Web of Conferences, 279, 11004.  \n- Williams, M., Davids, B., Lotay, G., et al. 2023, PhRvC, 107, 035803.  \nXiong, Z., Mart'ınez-Pinedo, G., Just, O., et al. 2024, PhRvL, 132, 192701.  \n- Zhang, L.Y., He, J.J., Kusakabe, M., et al. 2022, ApJ, 927, 92.", 'A. TABLES': "Table 1. Experimental cross sections for 160 Dy( p, γ ) 161 Ho and 162 Er( p, γ ) 163 Tm compared with TALYS calculations using default and 'TALYS optimized' inputs .Table 2. Selected models in TLAYS varied in this work (first column), corresponding TALYS keywords (second column) and their ranges (third column), and the optimized model parameters reproducing experimental reaction cross section of the A ≈ 160 mass region (fourth column).  \nTable 3. Deduced stellar rate (s -1 ) of the 157 Ho( γ , p ) 156 Dy, 159 Ho( γ , p ) 158 Dy, 163 Tm( γ , p ) 162 Er and 165 Tm( γ , p ) 164 Er in the range of T 9 = [0.1,10].Table 4. Coefficients of JINA analytical function for photo-nuclear reaction rates of 157 Ho( γ, p ) 156 Dy, 159 Ho( γ, p ) 158 Dy, 163 Tm( γ, p ) 162 Er and 165 Tm( γ, p ) 164 Er in the range of T 9 =[0.1, 10]"}