This paper presents a systematic evaluation of the ability of theoretical models to reproduce experimental Gamow-Teller transition strength distributions measured via (n,p)-type charge-exchange reactions at intermediate beam energies. The focus is on
transitions from stable nuclei in the pf shell (45<A<64). The impact of deviations between experimental and theoretical Gamow-Teller strength distributions on derived stellar electron-capture rates at densities and temperatures of relevance for Type Ia and Type II supernovae is investigated. The theoretical models included in the study are based on the shell-model, using the KB3G and GXPF1a interactions, and quasiparticle random-phase approximation (QRPA) using ground-state deformation parameters and masses from the finite-range droplet model.
The proportionality between differential cross sections at vanishing linear momentum transfer and Gamow-Teller transition strength, expressed in terms of the textit{unit cross section} ($hat{sigma}_{GT}$) was studied as a function of target mass numb
er for ($t$,$^{3}$He) and ($^{3}$He,$t$) reactions at 115 $A$MeV and 140 $A$MeV, respectively. Existing ($^{3}$He,$t$) and ($t$,$^{3}$He) data on targets with mass number $12leq Aleq 120$ were complemented with new and reevaluated ($t$,$^{3}$He) data on proton, deuteron, $^{6}$Li and $^{12}$C targets. It was found that in spite of the small difference in beam energies between the two probes, the unit cross sections have a nearly identical and simple dependence on target mass number $A$, for $Ageq 12$: $hat{sigma}_{GT}=109/A^{0.65}$. The factorization of the unit cross sections in terms of a kinematical factor, a distortion factor and the strength of the effective spin-isospin transfer nucleus-nucleus interaction was investigated. Simple phenomenological functions depending on mass number $A$ were extracted for the latter two. By comparison with plane and distorted-wave Born approximation calculations, it was found that the use of a short-range approximation for knock-on exchange contributions to the transition amplitude results in overestimated cross sections for reactions involving the composite ($^{3}$He,$t$) and ($t$,$^{3}$He) probes.
Gamow-Teller and dipole transitions to final states in 13B were studied via the 13C(t,3He) reaction at Et = 115 AMeV. Besides the strong Gamow-Teller transition to the 13B ground state, a weaker Gamow-Teller transition to a state at 3.6 MeV was found
. This state was assigned a spin-parity of 3/2- by comparison with shell-model calculations using the WBP and WBT interactions which were modified to allow for mixing between nhw and (n+2)hw configurations. This assignment agrees with a recent result from a lifetime measurement of excited states in 13B. The shell-model calculations also explained the relatively large spectroscopic strength measured for a low-lying 1/2+ state at 4.83 MeV in 13B. The cross sections for dipole transitions up to Ex(13B)= 20 MeV excited via the 13C(t,3He) reaction were also compared with the shell-model calculations. The theoretical cross sections exceeded the data by a factor of about 1.8, which might indicate that the dipole excitations are quenched. Uncertainties in the reaction calculations complicate that interpretation.
The 64-Zn(t,3-He) reaction has been studied using a secondary triton beam of 115 MeV/nucleon to extract the Gamow-Teller transition-strength distribution to 64-Cu. The results were compared with shell-model calculations using the pf-shell effective i
nteractions KB3G and GXPF1A and with existing data from the 64-Zn(d,2-He) reaction. Whereas the experimental results exhibited good consistency, neither of the theoretical predictions managed to reproduce the data. The implications for electron-capture rates during late stellar evolution were investigated. The rates based on the theoretical strength distributions are lower by factors of 3.5-5 compared to the rates based on experimental strength distributions.
Gamow-Teller transitions from 24Mg to 24Na were studied via the (t,3He) reaction at 115 AMeV using a secondary triton beam produced via fast fragmentation of 150 AMeV 16O ions. Compared to previous (t,3He) experiments at this energy that employed a p
rimary alpha beam, the secondary beam intensity is improved by about a factor of five. Despite the large emittance of the secondary beam, an excitation-energy resolution of ~200 keV is achieved. A good correspondence is found between the extracted Gamow-Teller strength distribution and those available from other charge-exchange probes. Theoretical calculations using the newly developed USDA and USDB sd-shell model interactions reproduce the data well.
Differential cross sections for transitions of known weak strength were measured with the (3He,t) reaction at 420 MeV on targets of 12C, 13C, 18O, 26Mg, 58Ni, 60Ni, 90Zr, 118Sn, 120Sn and 208Pb. Using this data, it is shown the proportionalities betw
een strengths and cross sections for this probe follow simple trends as a function of mass number. These trends can be used to confidently determine Gamow-Teller strength distributions in nuclei for which the proportionality cannot be calibrated via beta-decay strengths. Although theoretical calculations in distorted-wave Born approximation overestimate the data, they allow one to understand the main experimental features and to predict deviations from the simple trends observed in some of the transitions.
The Gamow-Teller strength for the transition from the ground state of 13C to the T=1/2, J^pi=3/2- excited state at 3.51 MeV in 13N is extracted via the 13C(3He,t) reaction at 420 MeV. In contrast to results from earlier (p,n) studies on 13C, a good a
greement with shell-model calculations and the empirical unit cross section systematics from other nuclei is found. The results are used to study the analog 13N(e-,v_e)13C reaction, which plays a role in the pre-explosion convective phase of type Ia supernovae. Although the differences between the results from the (3He,t) and (p,n) data significantly affect the deduced electron-capture rate and the net heat-deposition in the star due to this transition, the overall effect on the pre-explosive evolution is small.
The 24Mg(3He,t)24Al reaction has been studied at E(3He)=420 MeV. An energy resolution of 35 keV was achieved. Gamow-Teller strengths to discrete levels in 24Al are extracted by using a recently developed empirical relationship for the proportionality
between Gamow-Teller strengths and differential cross sections at zero momentum transfer. Except for small discrepancies for a few weak excitations, good agreement with previous 24Mg(p,n) data and nuclear-structure calculations using the USDA/B interactions in the sd shell-model space is found. The excitation energy of several levels in 24Al of significance for determination of the 23Mg(p,gamma)24Al thermonuclear reaction rate were measured. Results are consistent with two of the three previous (3He,t) measurements, performed at much lower beam energies. However, a new state at Ex(24Al)=2.605(10) MeV was found and is the third state above the proton separation energy.
