Re-estimation of 180 Ta nucleosynthesis in light of newly constrained reaction rates

and γ -ray strength functions below the neutron thresholds in 180 , 181 , 182 Ta are used as input in the nuclear reaction code TALYS. These experimental average quantities are utilized in the calculations of the 179 , 180 , 181 Ta radiative neutron capture cross sections. From the latter, astrophysical Maxwellian-averaged ( n , γ ) cross sections (MACS) and reaction rates are extracted, which in turn are used in large astrophysical network calculations to probe the production mechanism of 180 Ta. These calculations are performed for two scenarios, the s -process production of 180 , 181 Ta in Asymptotic Giant Branch (AGB) stars and the p -process nucleosynthesis of 180 Ta m in Type-II supernovae. Based on the results from this work, the s -process in stellar evolution is considered negligible in the production of 180 Ta m whereas 181 Ta is partially produced by AGB stars. The new measurements strongly constrain the production and destruction rates of 180 Ta m at p -process temperatures and conﬁrm signiﬁcant production of nature’s rarest stable isotope 180 Ta m by the p -process.


Introduction
A small number of naturally occurring neutron-deficient nuclides with Z ≥ 34, referred to as p-nuclei, cannot be produced by neutron-capture processes [1]. Instead, these stable nuclides with 74 ≤ A ≤ 196 are thought to be produced by the photodisintegration (p-process) of slow-neutron capture (s-process) and rapidneutron capture (r-process) seed nuclei [1]. However, for 138 La and 180 Ta, for instance, the p-process is not sufficient to explain their observed solar abundances and additional processes are invoked.
While the situation for 180 Ta is not clear, it was shown that for 138 La the photodisintegration of seed nuclei is not efficient enough but that neutrino (ν) captures during the p-process in Type-II supernovae may be responsible for its galactic enrichment [2][3][4].
A peculiar feature of 180 Ta is that it is the rarest isotope found in the solar system, with an isotopic abundance of only 0.012% existing in a J π = 9 − isomeric state at an excitation energy E x = 77 keV with a half-life of ≈10 15 yr.
The 180 Ta production mechanism invokes controversy since calculations show that several nucleosynthesis processes, sometimes exclusively, can reproduce the observed 180 Ta abundance [5], making it a particularly interesting case to study. The s-, r-and p-processes in high-density, high-temperature environments, have all been proposed to explain the synthesis of 180 Ta. It has been theoretically shown that 180  clusively explained by the p-process [2,6,7]. In explosive environments, neutrino captures and scattering reactions, which include 180 Hf(ν e , e) 180 Ta and 181 Ta(ν, ν n) 180 Ta, have also been proposed to significantly contribute to its synthesis [2,5,[8][9][10]. Additionally, the s-process has been invoked to explain the production of 180 Ta, mostly via branching in 179 Hf through the reaction 179 Hf(β − ) 179 Ta(n, γ ) 180 Ta and/or 179 Hf(n, γ ) 180 Hf m (β − ) 180 Ta [11][12][13].
Since the astrophysical sites for the nucleosynthesis of 180 Ta remain unknown, a combination of the above processes is undeniably possible. However, the significance of individual processes cannot be clearly determined, as a result of the uncertainties on the reaction rates for 180 Ta due to the unavailability of experimental data, e.g. the radiative neutron capture rates of 179,180 Ta isotopes or other nuclear ingredients needed to constrain these rates, such as the nuclear level density (NLD) and γ -ray strength function (γ SF) [3]. No NLD and γ SF data existed below the neutron separation energy (S n ) for 180 Ta, while for 181 Ta no data were available for E x < 5.8 MeV until very recently when comprehensive measurements were published for 180,181,182 Ta [14,15]. The NLD is described as the average number of nuclear energy levels as a function of excitation energy E x [16,17], while the γ SF gives a measure of the average transition probability for an electromagnetic de-excitation of the nucleus [18]. In the absence of direct cross section measurements, both properties are critical for constraining the radiative neutron capture cross section within the Hauser-Feshbach formalism [19] which is implemented in the nuclear reaction code TALYS [20].
In this letter, the recently measured NLDs and γ SFs in 180,181,182 Ta [14] are used to determine the 179,180,181 Ta(n, γ ) cross sections of astrophysical interest. From these, the Maxwellianaveraged cross sections (MACS) are obtained and used in stellar evolution calculations to investigate the role of the s-process in the nucleosynthesis of 180,181 Ta. The p-process nucleosynthesis for 180 Ta is studied on the basis of the Type-II supernova (SNII) model.

Experiments and analysis
In this work, the results of experimental NLDs and γ SFs for 180,181,182 Ta [14] are being used, and only a brief summary is provided on the measurements of these quantities. 3 He and deuteron beams impinge on a natural self-supporting 181 Ta metallic foil of 0.8 mg/cm 2 thickness. The reactions with deuteron beams are with i) 12 3 He γ ) 181 Ta and 181 Ta( 3 He, αγ ) 180 Ta. The light-charged ejectiles in coincidence with γ -rays were detected with the array of 64 E − E silicon particle telescopes SiRi [21]. The γ -rays were recorded using the high-efficiency multi-detector NaI(Tl) array CACTUS [22]. The NLDs and γ SFs were measured for each of the six distinct reactions which populated excited states in 180,181,182 Ta.
The measured particle energies in SiRi were converted to E x of the residual 180,181,182 Ta nuclei from reaction kinematics, Q-values and energy losses. The γ -rays were measured in coincidence with CACTUS. The respective E x versus γ -ray energy (E γ ) matrices are extracted from the particle-γ coincidence events. The Oslo Method [23] is applied to the matrices to extract simultaneously the NLDs and the γ SFs, through several iterative methods. The main steps of the Oslo Method include: 1) unfolding the continuum γ -ray spectrum based on the known detector multiple response functions [24] 2) extraction of primary γ -rays from the unfolded γ -ray spectra using the iterative procedure called the first generation method [24] 3) simultaneous extraction of the NLD and the γ -ray transmission coefficients from the primary γ -ray matrix, and 4) the normalization of the NLD and the γ -ray transmission coefficient using the average s-wave neutron resonance data [23,25]. Detailed discussions of the Oslo Method are found in refs. [22][23][24][25]. The total NLD at the neutron separation energy, ρ(S n ), was extracted from measured s-wave spacing using three different models, the Back-shifted Fermi-Gas (BSFG) [26], Constant Temperature+Fermi Gas (CT+FG) [20], and Hartree-Fock-Bogoliubov plus Combinatorial (HFB) [27] models. The range of results from these models and their normalizations provide the upper and lower limits in the NLDs and γ SFs.

(n, γ ) cross sections
The experimental NLDs and γ SFs from each reaction, taking into account their uncertainties, are now used as input parameters into the TALYS [20] reaction code (version 1.9). The have been calculated. The calculations are based on the Hauser-Feshbach statistical emission model [19] which assumes that the capture reactions occur by means of a compound nuclear system that reaches a statistical equilibrium. The key ingredients to the calculation of (n, γ ) cross sections are nuclear structure properties i.e. mass, deformation, low-lying level scheme, E x , J π , NLDs, γ SFs and optical model potentials. The neutron capture reaction cross (1) The neutron transmission coefficient, T μ n (E, J π ), is significantly larger than the γ -ray transmission coefficient, T μ γ (E, J π ), above S n , and depends on the total angular momentum J , parity π , and energy E x of the compound system. The target and projectile spins are given by subscripts I and n. The relative wave number π λ 2 = 0.6566/[m · E μ (MeV)] barn, where m and E μ are the reduced mass of the I μ + n system and the center-ofmass energy at a level μ, respectively [28]. The γ -ray transmission coefficient, T μ γ (E, J π ), in Eq. (1) for the decay of the compound nuclear state J π into any combination of final accessible states is given by the sum of T μ X L (E γ ) over discrete states μ plus the integral of T X L (E γ ) over the nuclear level density ρ(E x − E γ ) in the continuum, for a given multipolarity The global neutron optical model potential of Ref. [20,29] was used for all nuclei under discussion, as well as the Hofmann-Richert-Tepel-Weidenmüller (HRTW) model [30] for width fluctuation corrections in the compound nucleus calculation. Shown in Fig. 1, are the resulting 181 Ta(n, γ ) 182 Ta, 180 Ta m (n, γ ) 181 Ta and 179 Ta(n, γ ) 180 Ta m cross sections. The newly obtained experimental 181 Ta(n, γ ) 182 Ta cross sections, using the BSFG, CT+FG (1 & 2) and HFB normalizations in Fig. 1 (a) show good agreement with each other and with previous Time-of-Flight (ToF) [31,32] and activation [33] measurements.
The experimental 180 Ta m (n, γ ) cross sections from Ref. [34] are also shown for comparison and agree well with the present cross sections ( Fig. 1 (b)). While no comparative experimental data exist, the 179 Ta(n, γ ) 180 Ta m cross sections ( Fig. 1 (c)) are in good agreement with those predicted using microscopic NLD models [35]. The agreement between our results and direct measurements validates that experimental NLDs and γ SFs can be used to successfully obtain (n, γ ) cross sections and has reliably been used over different mass regions [36][37][38]. This brings further evidence that this technique can be used when no direct measurements of cross sections are possible [4,39,40]. The (n, γ ) cross sections from the experimental NLDs and γ SFs obtained using the different reaction channels, are consistent with each other. This is indicative of the robustness of the Oslo Method but also that the results are independent of beam type and beam energies.
In hot stellar environments, the target nucleus is not confined to its ground state but exists in a distribution of thermally excited states μ. At high temperatures T , the relative thermal velocities ν T and excitation energies E μ x of nuclei obey a Maxwell-Boltzmann distribution and the thermonuclear reaction rate for neutron induced reactions, in units of cm 3 mol −1 s −1 , is given by [28] where N A is the Avogadro's number and k is the Boltzmann constant. The temperature-dependent normalized partition function ify the state distribution of the target. When μ = 0, Eq. (2) gives the reaction rate for the target in its ground state (i.e. laboratory reaction rates). The thermonuclear reaction rates were computed for the astrophysical temperatures T 9 in GK (T 9 ≡ T /10 9 K) ranging from 0.0001 ≤ T 9 ≤ 10. For targets in thermal equilibrium, where the principle of detailed balance is valid [28], the reverse photo-neutron emission rates 180,181,182 Ta(γ , n) are also obtained.
The astrophysical MACS σ v n,γ /ν T , where ν T is the relative thermal velocity ν T = 2kT /m, were calculated for each data set of all the 179,180,181 Ta(n, γ ) reactions, at the s-and p-process ther-

Nucleosynthesis application
Here, it is not the intention to give a complete review of the 180 Ta nucleosynthesis in different astrophysical sites, but rather to re-estimate, in light of the newly determined 179 Ta(n, γ ) 180 Ta gs,m , 180 Ta gs,m (n, γ ) 181 Ta and 181 Ta(n, γ ) 182 Ta rates, the 180 Ta and 181 Ta yields originating from the s-process in Asymptotic Giant Branch (AGB) stars and the p-process in massive stars exploding as Type-II supernovae. Both processes are studied below.

S-process production of 180 Ta m and 181 Ta
For the s-process production of 180 Ta m and 181 Ta, we have performed stellar evolution calculations to follow the complex production of 180 Ta during the thermally pulsing AGB phase. AGB models have been computed with the STAREVOL code [42,43] using an extended s-process reaction network of 411 species and the same input physics as described in Ref. [44]. We focus here on a standard 2 M [Fe/H] = −0.5 model star known to produce the main s-process elements ranging between A = 90 and A = 204. In the present calculation, a diffusion equation is used to simulate the partial mixing of protons in the C-rich layers at the time of the third dredge-up. Following the formalism of Eq. (9) of Ref. [44], the diffusive mixing parameters adopted in our calculations are D min = 10 9 cm 2 /s and p = 5, where D min is the value of the diffusion coefficient at the innermost boundary of the convective envelope and p is an additional free parameter defining the slope of the exponential decrease of the overshoot diffusion coefficient with depth.
When not available experimentally, the cross sections were calculated within the statistical Hauser-Feshbach model with the TALYS reaction code [20,45]. The TALYS calculations were also used systematically to deduce from the laboratory neutron capture cross sections the stellar rates by allowing for the possible thermalization of low-lying states in the target nuclei. We note that at low temperature, the non-thermalization of the isomeric states of 26 Al,85 Kr,115 In, 176 Lu and 180 Ta is introduced explicitly in the reaction network [12,46]. Despite some studies predicting the thermalization of the 180 Ta ground and isomeric states at a temperature exceeding 25 keV [47,48], we assume here that both states are not thermalized at the temperatures found in our 2 M [Fe/H] = −0.5 model star. The temperature-and densitydependent β-decay and electron capture rates in stellar conditions were taken from Ref. [49] with the update of Ref. [50]. Most importantly, the factor of about 3 for the uncertainties associated with the 179 Hf(β − ) 179 Ta, as well as the 20-30% impact on the 179 Ta(EC) 179 Hf decay rate are taken into account following the uncertain log f t transition rates considered in Ref. [50].  overall surface enrichment of s-only nuclei with an overabundance of about 1.7-2 dex, 180 Ta is seen to be strongly underabundant by a factor of about 100 in comparison with s-nuclei. As shown in Fig. 3, illustrating the profiles of 180 Ta m and 181 Ta inside the star, 180 Ta m is not present in the envelope (M r 0.67 M ), but its abundance peaks at about 2 dex in a thin layer below the convective envelope. This region lies just below the bottom of the thermal pulse where the temperature is high enough to favor a significant decay of 179 Hf into 179 Ta followed by a neutron capture, with the neutron stemming from the 22 Ne(α, n) 25 Mg reaction, hence a production of 180 Ta. Note that at a temperature 0.1 T 9 , the 179 Hf(β − ) 179 Ta decay timescale is about 2 Gyr while at 0.3 T 9 , it falls to about 25 yr. However, the neutron captures take place below the thermal pulse where 22 Ne has been produced from the previous thermal pulse. Consequently this 180 Ta-rich region is not engulfed in the convective pulse, nor by the third dredge-up bringing the ashes of the interpulse and pulse nucleosynthesis up to the surface. Similar results concerning the absence of 180 Ta surface enrichment are found for AGB stars with an initial mass of 1.5 to 3.5 M . For this reason, contributions of low-mass AGB stars to the 180 Ta galactic enrichment can be expected to be relatively negligible.

P-process production of 180 Ta
Now we study the p-process nucleosynthesis on the basis of the Type-II supernova model, as described in [2,6,51], i.e. a model for a Z 8 M helium star (main sequence mass of about 25 M ) evolved from the beginning of core He burning to the supernova explosion. We consider the 25 layers in the O/Ne-rich zone with explosion temperatures peaking between 1.7-3.3 T 9 responsible for the production of the p-elements. Their total mass is about 0.75 M . The deepest layer is located at a mass of about 1.94 M , which is far enough from the mass cut for all the nuclides produced in this region to be ejected during the explosion. All nucleosynthesis calculations have assumed here the absence of neutrinos.  balance relation) and their associated uncertainties used in the present simulation correspond to the present experimentally constrained values (see Sect. 3). Only these rates are modified in the simulation and different combinations considered to estimate their impact on the nucleosynthesis. The resulting uncertainties are seen in Fig. 4 to give rise to a rather small error bar on the 180 Ta overproduction factor. As shown in Table 1, the new experimentally constraints essentially affect the 179 Ta(n, γ ) MACS by increasing it by a factor of about 1.5 with respect to the only previously available theoretical estimates (KaDoNiS). Such an increase also impact the reverse 180 Ta(γ , n) destruction rate leading to a decrease of the 180 Ta m by a factor 1.35 with respect to the yields that would have been obtained with the KaDoNiS rates.
The final 180 Ta overproduction is clearly compatible with the p-process enrichment of the other p-nuclei (even neglecting the neutrino effects). Two major effects may still affect the total abundance of 180 Ta given in Fig. 4. The first one concerns the possible increase of the 180 Ta production by neutrino captures [2,10]. For a total neutrino luminosity L ν = 2.3 × 10 52 ergs s −1 , and neutrino temperatures of T ν e = 2.8 MeV and Tν e = T ν μ,τ = 4.0 MeV [10], we find that the 180 Ta abundance is increased by a factor of 1.3, and for a luminosity ten times larger, L ν = 2.3 × 10 53 ergs s −1 , by a factor of 4. The charged current capture on 180 Hf is found to be the major contributor, while the neutral current on 181 Ta leads to a contribution twice smaller than the charged current one, as also found in Ref. [10]. Obviously, the impact of this extra production is still subject to all the uncertainties related to the neutrino physics, and in particular to the neutrino luminosity, temperature, oscillation and interaction cross sections. Note however that the recent measurement of the 180 Hf Gamow-Teller strength significantly constrain the 180 Hf(ν e , e -) rate [9].
A second effect arises from the freeze-out of the thermal equilibrium between the isomeric and ground states of 180 Ta at temperatures below 0.3-0.4 T 9 [3,47,48]. The 180 Ta yields displayed in Fig. 4 are obtained under the assumption that 180 Ta remains equilibrated until the photoreactions responsible for its production and destruction freeze out. The abundance left over in the isomeric state critically depends on the temperature at which the ground and isomeric states stop thermalizing. For a critical temperature of 0.3-0.4 T 9 , about 40% of the total 180 Ta abundance initially produced during the p-process ends up in the long-lived isomeric state, and consequently contributes to the galactic enrichment (for more details, see Ref. [3]). The conclusion that 180 Ta is essentially produced by the p-process is considered to be robust, and to hold irrespective of the intricacies and uncertainties related to the rates of the main photodisintegrations responsible for its production and destruction, to the thermal equilibration of 180 Ta, or to the details of the SNII models, at least in their spherically symmetric onedimensional approximation.

Summary
In summary, the 180,181,182 Ta NLDs and γ SFs obtained experimentally [14] are used as input parameters in the TALYS reaction code to calculate the 179,180,181 Ta radiative (n, γ ) cross sections. From these, the Maxwellian averaged (n, γ ) cross sections (MACS) and reaction rates of astrophysical interest are obtained. The compatibility of the new measurements with other experimental data supports the approach to use statistical properties i.e. NLDs and γ SFs to estimate radiative capture cross sections, MACS and reaction rates. The latter are used in s-process calculations in AGB stars and p-process simulations in Type-II supernovae to investigate the nucleosynthesis of 180 Ta. The newly constrained reaction rates from this work show that the s-process contribution in lowmass AGB stars to the production of 180 Ta galactic enrichment is negligible and that 181 Ta is partially produced by AGB stars. The p-process nucleosynthesis of nature's rarest stable isotope 180 Ta in Type-II supernovae using new constraints from the current experimental measurements is significant and therefore suggests the p-process to be the fundamental production mechanism of 180 Ta m in the universe. Detailed calculations in additional models stars both for AGBs and SN progenitors will further help in understanding the overall 180 Ta enrichment of the galaxy.