Gamow-Teller Transition Strengths Research Articles

What can we learn from recent 2ν β β experiments?*

Abstract Recent measurements of the two neutrino double beta decay high precision electron spectra, combined with charge exchange or β-decay experimental data, have revealed severe constraints across current nuclear many body calculations. Our calculations show that the quasi-particle random phase approximation (QRPA) approach can adequately reproduce the measured spectra for the two open shell nuclei, Se and Mo. For the closed shell nucleus Xe, QRPA can also reproduce the spectra with proper treatments. Considering the high-lying state reduction, we also find that the nuclear shell model can also adequately reproduce the spectra and Gamow-Teller transition strength under a unique quenched axial-vector coupling constant . For Xe, we find that flipping the sign for the decay strength causes the spectra to go beyond the so-called high-lying state dominance hypothesis. These results call for future high precision measurements of charge-exchange reactions.

INVESTIGATION OF GAMOW-TELLER STRENGTHS FOR A=34 AND A=37 NUCLEI

In this work, the Gamow-Teller transition strength distributions in sd-shell region were investigated by using shell model. The calculations of B(GT) and their accumulated sum ∑B(GT) for the nuclei 34Ar→34Cl, 34S→34Cl, 37Cl→37Ar, and 37Ca→37K were performed using the shell model by utilizing the USDB and USDA effective interactions in the sd-shell. The transitions for the nuclei are studied. The results for the B(GT) and ∑B(GT) are discussed and compared to the most recent observed data. The measured GT distributions and the cumulative transition intensities B(GT) are in a fair amount of agreement with the theoretical calculations. We have established a qualitative agreement for the individual transformations, and the measured cumulative transformation strengths nearly match the observed ones.

β^{+} Gamow-Teller Strengths from Unstable ^{14}O via the (d,^{2}He) Reaction in Inverse Kinematics.

For the first time, the (d,^{2}He) reaction was successfully used in inverse kinematics to extract the Gamow-Teller transition strength in the β^{+} direction from an unstable nucleus. The new technique was made possible by the use of an active-target time-projection chamber and a magnetic spectrometer, and opens a path to addressing a range of scientific challenges, including in astrophysics and neutrino physics. In this Letter, the nucleus studied was ^{14}O, and the Gamow-Teller transition strength to ^{14}N was extracted up to an excitation energy of 22MeV. The data were compared to shell-model and state-of-the-art coupled-cluster calculations. Shell-model calculations reproduce the measured Gamow-Teller strength distribution up to about 15MeV reasonably well, after the application of a phenomenological quenching factor. In a significant step forward to better understand this quenching, the coupled-cluster calculation reproduces the full strength distribution well without such quenching, owing to the large model space, the inclusion of strong correlations, and the coupling of the weak interaction to two nucleons through two-body currents.

Gamow-Teller decay of Te142 to I142

The β decay of Te90142 to I89142 was investigated for the first time. The parent nucleus was produced by the in-flight fission of a U238 beam with an energy of 345 MeV per nucleon, impinging on a Be9 target at the Radioactive Isotope Beam Factory of RIKEN. Excited states in I142 were established by β-delayed γ-ray spectroscopy. The observed (1+) states in I142 could be interpreted to be predominantly the ν0h9/2⊗π0h11/2 configuration formed by a Gamow-Teller transition between a neutron in the 0h9/2 orbital and a proton in the 0h11/2 orbital. Additional features of the (1+) states are discussed by comparing with neighboring heavier isotones, such as Cs144 and La146. In the context of deformed shell-model calculations, the (11+) state is closely related to the ν[5,3,2]3/2⊗π[5,5,0]1/2 configuration, which may be related to the weak Gamow-Teller transition strength.1 MoreReceived 30 August 2022Revised 16 November 2022Accepted 11 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.014311©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeta decayEnergy levels & level densitiesNuclear structure & decaysNucleon-nucleon interactionsShell modelProperties90 ≤ A ≤ 149TechniquesRadiation detectorsRadioactive beamsSpectrometers & spectroscopic techniquesNuclear Physics

Probing spin-isospin excitations in proton-rich nuclei via theC11(p,n)N11reaction

Tracking the evolution of nuclear properties away from stability serves as a valuable test for nuclear models. In the present work, the $(p,n)$ charge-exchange reaction was used to test the extraction of ${\ensuremath{\beta}}^{\ensuremath{-}}$ Gamow-Teller transition strengths, $B(\mathrm{GT})$, from proton-rich unstable isotopes, and the resulting $B(\mathrm{GT})$ values were compared to shell-model and ab initio calculations. The $^{11}\mathrm{C}(p,n)^{11}\mathrm{N}$ reaction was measured in inverse kinematics at 95 MeV/u at the National Superconducting Cyclotron Laboratory. The $B(\mathrm{GT})$ values to the ${\frac{1}{2}}^{\ensuremath{-}}$ state at 0.73 MeV and the ${\frac{3}{2}}^{\ensuremath{-}}$ state at 2.86 MeV in $^{11}\mathrm{N}$ were determined to be $0.18{(1)}^{\mathrm{stat}}{(3)}^{\mathrm{sys}}$ and $0.18{(1)}^{\mathrm{stat}}{(4)}^{\mathrm{sys}}$, respectively. These results are consistent with shell-model calculations using the wbp interaction after introducing a phenomenological quenching factor and with ab initio variational Monte Carlo calculations using the $NV2+3I{a}^{*}$ $NN$ and $3N$ interactions without any scaling. Additionally, this result is consistent with the $B(\mathrm{GT})$ values extracted from mirror $^{11}\mathrm{B}(n,p)$ and $^{11}\mathrm{B}(t,^{3}\mathrm{He})$ reactions. This experiment demonstrates the feasibility of using the $(p,n)$ probe in inverse kinematics to extract $B(\mathrm{GT})$ from proton-rich nuclei, although improved background suppression will be important in future experiments.

How effective is the Brink–Axel hypothesis for astrophysical weak rates?

Abstract We explore the effectiveness of the Brink–Axel hypothesis (BAH) for the computation of stellar electron capture (EC) and β-decay (BD) rates, namely that the transition strength function depends only upon the transition energy and not upon the details of the initial state. For this purpose, we calculated Gamow–Teller (GT) strength distributions for a selection of sd-shell nuclides, using two different microscopic models, namely the proton–neutron quasiparticle random phase approximation and the full configuration-interaction shell model, taking into account the first 100 states of both the initial and final nuclides. The GT transition strengths among these levels evolve with initial state energy. These transition strength functions we folded into weak-interaction mediated rates in stellar matter, specifically EC and BD rates, for a range of densities 10 g cm−3 ⩽ ρ ⩽ 1011 g cm−3 and range of temperatures 1 GK ⩽ T ⩽ 30 GK. When transitions from excited states were approximated using the BAH, augmented by so-called ‘back-resonance’ transitions, the rates were affected by up to three orders of magnitude or more at high temperatures and densities. Thus the BAH is not a reliable approximation for the calculation of stellar rates, especially in high temperature–density environments.

First observation of the π0h11/2⊗ν0h9/2 partner orbital configuration in the odd-odd I138 nucleus

The β-decay scheme of Te138 and the level structure of I138 is reported for the first time. The experiment was performed at the Radioactive Isotope Beam Factory of RIKEN, as one of the EUROBALL-RIKEN Cluster Array campaigns. Secondary radioactive ions, including Te138 and Sb138, were produced by the in-flight fission of a U238 beam with the energy of 345 MeV per nucleon. From the β decay of Te138, the level scheme of I138 was supplemented with new spin and parity assignments, such as the low-lying negative-parity states and a positive-parity 1+ state. This 1+ state can be interpreted as being associated with the π0h11/2⊗ν0h9/2 partner orbital configuration populated by the Gamow-Teller transition between a neutron in the 0h9/2 orbital and a proton in the 0h11/2 orbital. Details of the structure of I138 are discussed in terms of the proton-neutron interactions and Gamow-Teller transition strength within the theoretical context of shell-model calculations.Received 5 December 2021Accepted 16 March 2022DOI:https://doi.org/10.1103/PhysRevC.105.034334©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeta decayNuclear structure & decaysProperties90 ≤ A ≤ 149TechniquesRadiation detectorsRadioactive beamsShell modelSpectrometers & spectroscopic techniquesNuclear Physics

Shell-model calculation of Mo100 double- β decay

For the first time, the calculation of the nuclear matrix element of the double-$\beta$ decay of $^{100}$Mo, with and without the emission of two neutrinos, is performed in the framework of the nuclear shell model. This task is accomplished starting from a realistic nucleon-nucleon potential, then the effective shell-model Hamiltonian and decay operators are derived within the many-body perturbation theory. The exotic features which characterize the structure of Mo isotopes -- such as shape coexistence and triaxiality softness -- push the shell-model computational problem beyond its present limits, making it necessary to truncate the model space. This has been done with the goal to preserve as much as possible the role of the rejected degrees of freedom in an effective approach that has been introduced and tested in previous studies. This procedure is grounded on the analysis of the effective single-particle energies of a large-scale shell-model Hamiltonian, that leads to a truncation of the number of the orbitals belonging to the model space. Then, the original Hamiltonian generates a new one by way of a unitary transformation onto the reduced model space, to retain effectively the role of the excluded single-particle orbitals. The predictivity of our calculation of the nuclear matrix element for the neutrinoless double-$\beta$ decay of $^{100}$Mo is supported by the comparison with experiment of the calculated spectra, electromagnetic transition strengths, Gamow-Teller transition strengths and the two-neutrino double-beta nuclear matrix elements.

Constraining the solar neutrino survival probability curve by using Li6 , Li7 , C12 , O18 , F19 , and Ca42 nuclear targets

Precise measurement of the survival probability ${P}_{ee}$ of solar electron neutrino (${\ensuremath{\nu}}_{e}$) as a function of its energy [${P}_{ee}({E}_{\ensuremath{\nu}e})$] is one of the key issues in neutrino physics. Current ${P}_{ee}$ data, due to their limited accuracy, still allow for nonstandard interactions (NSIs) to be alternatives to the standard one, which is based on the MSW-LMA prediction. In order to determine ${P}_{ee}$ values at several values of ${E}_{\ensuremath{\nu}e}$ with higher accuracy, we propose to use several target nuclei with different threshold energies for ${\ensuremath{\nu}}_{e}$ detection. We examined charged-current (CC) responses of various nuclei seeking the ones: (a) having large and concentrated Gamow-Teller (GT) transition strength in the low excitation-energy region, and (b) having appropriate and a variety of reaction $Q$ values, i.e., $\ensuremath{\approx}1$ to 17 MeV, in the (${\ensuremath{\nu}}_{e},{e}^{\ensuremath{-}}$) reaction. As a result, we found that systematic solar ${\ensuremath{\nu}}_{e}$ measurements with target nuclei $^{6}\mathrm{Li}$, $^{7}\mathrm{Li}$, $^{12}\mathrm{C}$, $^{18}\mathrm{O}$, $^{19}\mathrm{F}$, and $^{42}\mathrm{Ca}$ can put strong constraints on the ${P}_{ee}({E}_{\ensuremath{\nu}e})$ curve and thus on these NSI models. In addition, we notice that three of these nuclei, $^{6}\mathrm{Li}$, $^{7}\mathrm{Li}$, and $^{12}\mathrm{C}$, have large and concentrated neutral-current (NC) responses with detection threshold-energies of 3.56, 0.48, and 15.11 MeV, respectively. Note that the NC measurement is flavor independent. Thus, the measured results should represent the original strength of ${\ensuremath{\nu}}_{e}$ from the Sun.

Tensor force role in β decays analyzed within the Gogny-interaction shell model

Background: The half-life of the famous $^{14}$C $\beta$ decay is anomalously long, with different mechanisms: the tensor force, cross-shell mixing, and three-body forces, proposed to explain the cancellations that lead to a small transition matrix element. Purpose: We revisit and analyze the role of the tensor force for the $\beta$ decay of $^{14}$C as well as of neighboring isotopes. Methods: We add a tensor force to the Gogny interaction, and derive an effective Hamiltonian for shell-model calculations. The calculations were carried out in a $p$-$sd$ model space to investigate cross-shell effects. Furthermore, we decompose the wave functions according to the total orbital angular momentum $L$ in order to analyze the effects of the tensor force and cross-shell mixing. Results: The inclusion of the tensor force significantly improves the shell-model calculations of the $\beta$-decay properties of carbon isotopes. In particular, the anomalously slow $\beta$ decay of $^{14}$C can be explained by the isospin $T=0$ part of the tensor force, which changes the components of $^{14}$N with the orbital angular momentum $L=0,1$, and results in a dramatic suppression of the Gamow-Teller transition strength. At the same time, the description of other nearby $\beta$ decays are improved. Conclusions: Decomposition of wave function into $L$ components illuminates how the tensor force modifies nuclear wave functions, in particular suppression of $\beta$-decay matrix elements. Cross-shell mixing also has a visible impact on the $\beta$-decay strength. Inclusion of the tensor force does not seem to significantly change, however, binding energies of the nuclei within the phenomenological interaction.

Total absorption spectroscopy of the β decay of Zr101,102 and Tc109

The $\ensuremath{\beta}$ decay of $^{101,102}\mathrm{Zr}$ and $^{109}\mathrm{Tc}$ was studied using the technique of total absorption spectroscopy. The experiment was performed at the National Superconducting Cyclotron Laboratory using the Summing NaI(Tl) (SuN) detector in the first-ever application of total absorption spectroscopy with a fast beam produced via projectile fragmentation. The $\ensuremath{\beta}$-decay feeding intensity and Gamow-Teller transition strength distributions were extracted for these three decays. The extracted distributions were compared to three different quasiparticle random-phase approximation (QRPA) models based on different mean-field potentials. A comparison with calculations from one of the QRPA models was performed to learn about the ground-state shape of the parent nucleus. For $^{101}\mathrm{Zr}$ and $^{102}\mathrm{Zr}$, calculations assuming a pure shape configuration (oblate or prolate) were not able to reproduce the extracted distributions. These results may indicate that some type of mixture between oblate and prolate shapes is necessary to reproduce the extracted distributions. For $^{109}\mathrm{Tc}$, a comparison of the extracted distributions with QRPA calculations suggests a dominant oblate configuration. The other two QRPA models are commonly used to provide $\ensuremath{\beta}$-decay properties in $r$-process network calculations. This work shows the importance of making comparisons between the experimental and theoretical $\ensuremath{\beta}$-decay distributions, rather than just half-lives and $\ensuremath{\beta}$-delayed neutron emission probabilities, as close to the $r$-process path as possible.

β decay of the very neutron-deficient Ge60 and Ge62 nuclei

We report here the results of a study of the $\beta$ decay of the proton-rich Ge isotopes, $^{60}$Ge and $^{62}$Ge, produced in an experiment at the RIKEN Nishina Center. We have improved our knowledge of the half-lives of $^{62}$Ge (73.5(1) ms), $^{60}$Ge (25.0(3) ms) and its daughter nucleus, $^{60}$Ga (69.4(2) ms). We measured individual $\beta$-delayed proton and $\gamma$ emissions and their related branching ratios. Decay schemes and absolute Fermi and Gamow-Teller transition strengths have been determined. The mass excesses of the nuclei under study have been deduced. A total $\beta$-delayed proton-emission branching ratio of 67(3)% has been obtained for $^{60}$Ge. New information has been obtained on the energy levels populated in $^{60}$Ga and on the 1/2$^-$ excited state in the $\beta p$ daughter $^{59}$Zn. We extracted a ground state to ground state feeding of 85.3(3)% for the decay of $^{62}$Ge. Eight new $\gamma$ lines have been added to the de-excitation of levels populated in the $^{62}$Ga daughter.

Si25β+ -decay spectroscopy

$\beta$-decay spectroscopy provides valuable information on exotic nuclei and a stringent test for nuclear theories beyond the stability line. To search for new $\beta$-delayed protons and $\gamma$ rays of $^{25}$Si to investigate the properties of $^{25}$Al excited states. $^{25}$Si $\beta$ decays were measured by using the Gaseous Detector with Germanium Tagging system at the National Superconducting Cyclotron Laboratory. The protons and $\gamma$ rays emitted in the decay were detected simultaneously. A Monte Carlo method was used to model the Doppler broadening of $^{24}$Mg $\gamma$-ray lines caused by nuclear recoil from proton emission. Shell-model calculations using two newly developed universal \textit{sd}-shell Hamiltonians, USDC and USDI, were performed. The most precise $^{25}$Si half-life to date has been determined. A new proton branch at 724(4)~keV and new proton-$\gamma$-ray coincidences have been identified. Three $^{24}$Mg $\gamma$-ray lines and eight $^{25}$Al $\gamma$-ray lines are observed for the first time in $^{25}$Si decay. The first measurement of the $^{25}$Si $\beta$-delayed $\gamma$ ray intensities through the $^{25}$Al unbound states is reported. All the bound states of $^{25}$Al are observed to be populated in the $\beta$ decay of $^{25}$Si. Several inconsistencies between the previous measurements have been resolved, and new information on the $^{25}$Al level scheme is provided. An enhanced decay scheme has been constructed and compared to the mirror decay of $^{25}$Na and the shell-model calculations. The measured excitation energies, $\gamma$-ray and proton branchings, log~$ft$ values, and Gamow-Teller transition strengths for the states of $^{25}$Al populated in the $\beta$ decay of $^{25}$Si are in good agreement with the shell-model calculations, offering gratifyingly consistent insights into the fine nuclear structure of $^{25}$Al.

Stellar electron-capture rates based on finite-temperature relativistic quasiparticle random-phase approximation

The electron capture process plays an important role in the evolution of the core collapse of a massive star that precedes the supernova explosion. In this study, the electron capture on nuclei in stellar environment is described in the relativistic energy density functional framework, including both the finite temperature and nuclear pairing effects. Relevant nuclear transitions $J^\pi = 0^\pm, 1^\pm, 2^\pm$ are calculated using the finite temperature proton-neutron quasiparticle random phase approximation with the density-dependent meson-exchange effective interaction DD-ME2. The pairing and temperature effects are investigated in the Gamow-Teller transition strength as well as the electron capture cross sections and rates for ${}^{44}$Ti and ${}^{56}$Fe in stellar environment. It is found that the pairing correlations establish an additional unblocking mechanism similar to the finite temperature effects, that can allow otherwise blocked single-particle transitions. Inclusion of pairing correlations at finite temperature can significantly alter the electron capture cross sections, even up to a factor of two for ${}^{44}$Ti, while for the same nucleus electron capture rates can increase by more than one order of magnitude. We conclude that for the complete description of electron capture on nuclei both pairing and temperature effects must be taken into account.

Gamow-Teller strengths of some sd-shell nuclei in the shell model framework

The nuclear Gamow-Teller (GT) transition strength distributions B(GT)have been studied for some sd-shell nuclei in the (3He, t) charge-exchangereactions. The shell model calculations were performed by employing theUSDA and USDB effective interactions in the sd-model space. The results of B(GT) calculations reproduce the the experimental Gamow-Tellerstrength distributions well, while the calculated distribution of summedGT transition strengths were closely reproduce the observed ones.

Gamow-Teller transitions to Zr93 via the Nb93(t,He3+γ ) reaction at 115 MeV/u and its application to the stellar electron-capture rates

Electron-capture reactions play important roles in the late evolution of core-collapse supernovae. The electron-capture rates used in astrophysical simulations rely on theoretical calculations which have to be tested against and guided by experimental data. We report on the measurement of the Gamow-Teller strength distribution of the odd-mass nucleus $^{93}\mathrm{Nb}$ via the ($t,^{3}\mathrm{He}$ + $\ensuremath{\gamma}$) charge-exchange reaction at a beam energy of 115 MeV/u. The Gamow-Teller strength distributions were extracted up to an excitation energy in $^{93}\mathrm{Zr}$ of 10 MeV. The results were compared with shell-model and quasiparticle random-phase approximation (QRPA) calculations. The theoretical calculations fail to describe the details of the strength distribution, but estimate reasonably well the integrated Gamow-Teller transition strength. Electron-capture rates derived from the measured and theoretical strength distributions match reasonably well, especially at the higher stellar densities of importance for deleptonization during the collapse of the stellar core, since the electron-capture $Q$ value is close to zero and the Fermi energy sufficiently high to ensure that the details of the strength distribution do not have a strong impact on the derived rates. At stellar densities in excess of ${10}^{9}$ g/${\mathrm{cm}}^{3}$, the electron-capture rate based on a single-state approximation used in astrophysical simulations is slightly higher than the rates based on the data and the shell-model and QRPA calculations, likely due to the fact that the approximation includes temperature-dependent effects, which increase the rates. However, the difference is much smaller than that observed in recent studies of nuclei with $Zl40$ near $N=50$, suggesting that the single-state approximation does not account for Pauli-blocking effects for nuclei with $Zl40$ that are much stronger than those for $^{93}\mathrm{Nb}$ with $Z=41$.

Gamow–Teller Transition Strengths for Selected \({fp}\) Shell Nuclei

We have reported a systematic shell model description of the experimental Gamow-Teller transition strength for $^{44}$Sc $\rightarrow$ $^{44}$Ca, $^{45}$Ti $\rightarrow$ $^{45}$Sc, $^{48}$Ti $\rightarrow$ $^{48}$V, $^{66}$Co $\rightarrow$ $^{66}$Ni, and $^{66}$Fe $\rightarrow$ $^{66}$Co transitions using KB3G and GXPF1A interactions for $fp$ model space. In order to see the importance of higher orbital for $^{66}$Co $\rightarrow$ $^{66}$Ni and $^{66}$Fe $\rightarrow$ $^{66}$Co transitions, we have reported the shell model results with $fpg_{9/2}$ space using GXPF1Br+$V_{MU}$ interaction. We have obtained the qualitative agreement for the individual transitions, while the calculated summed transition strengths closely reproduce the observed ones.

Renormalization of the Gamow-Teller operator within the realistic shell model

In nuclear structure calculations, the choice of a limited model space, due to computational needs, leads to the necessity to renormalize the Hamiltonian as well as any transition operator. Here, we present a study of the renormalization procedure and effects of the Gamow-Teller operator within the framework of the realistic shell model. Our effective shell-model operators are obtained, starting from a realistic nucleon-nucleon potential, by way of the many-body perturbation theory in order to take into account the degrees of freedom that are not explicitly included in the chosen model space. The theoretical effective shell-model Hamiltonian and transition operators are then employed in shell-model calculations, whose results are compared with data of Gamow-Teller transition strengths and double-beta half-lives for nuclei which are currently of interest for the detection of the neutrinoless double-beta decay process, in a mass interval ranging from A=48 up to A=136. We show that effective operators are able to reproduce quantitatively the spectroscopic and decay properties without resorting to an empirical quenching neither of the axial coupling constant gA, nor of the spin and orbital gyromagnetic factors. This should assess the reliability of applying present theoretical tools to this problematic.

High-resolution study of the Gamow-Teller ( GT− ) strength in the Zn64(He3,t)Ga64 reaction

Gamow-Teller (GT) transitions starting from the ${T}_{z}=+2$ nucleus $^{64}\mathrm{Zn}$ to the ${T}_{z}=+1$ nucleus $^{64}\mathrm{Ga}$ were studied in a ($p,n$)-type ($^{3}\mathrm{He},t$) charge-exchange reaction at a beam energy of 140 MeV/nucleon and scattering angles close to ${0}^{\ensuremath{\circ}}$. Here, ${T}_{z}$ is the $z$ component of the isospin $T$. The experiment was conducted at the Research Center for Nuclear Physics (RCNP) in Osaka, Japan. An energy resolution of $\ensuremath{\approx}34$ keV was achieved by applying beam matching techniques to the Grand Raiden magnetic spectrometer system. With our good resolution, we could observe GT strength fragmented in many states up to an excitation energy of $\ensuremath{\approx}11$ MeV. By performing angular distribution analysis, we could identify states in $^{64}\mathrm{Ga}$ excited by GT transitions. The reduced GT transition strengths [$B$(GT) values] were calculated assuming the proportionality between the cross sections and the $B$(GT) values. Shell-model calculations using the GXPF1J interaction reproduced the $B$(GT) strength distribution throughout the spectrum. States with isospin $T=3$ were identified by comparing the $^{64}\mathrm{Zn}\text{(}{}^{3}\text{He,}t{\text{)}}^{64}\text{Ga}$ spectrum with a $^{64}\mathrm{Zn}(d,^{2}\mathrm{He})^{64}\mathrm{Cu}$ spectrum. Relative excitation energies of the corresponding structures are in good agreement, supporting the robustness of isospin symmetry in the mass number $A=64$ nuclei.

The (Li6,Li*6[3.56MeV]) reaction at 100 MeV/u as a probe of Gamow-Teller transition strengths in the inelastic scattering channel

Background: Inelastic neutrino-nucleus scattering is important for understanding core-collapse supernovae and the detection of emitted neutrinos from such events in earth-based detectors. Direct measurement of the cross sections is difficult and has only been performed on a few nuclei. It is, therefore, important to develop indirect techniques from which the inelastic neutrino-nucleus scattering cross sections can be determined. Purpose: This paper presents a development of the (Li-6,Li-6*[T = 1, T-z = 0, 0(+), 3.56 MeV]) reaction at 100 MeV/u as a probe for isolating the isovector spin-transfer response in the inelastic channel (Delta S = 1, Delta T = 1, Delta T-z = 0) from which the Gamow-Teller transition strengths from nuclei of relevance for inelastic neutrino-nucleus scattering cross sections can be extracted. Method: By measuring the Li-6 ejectile in a magnetic spectrometer and selecting events in which the 3.56 MeV gamma ray from the decay of the Li-6*[3.56 MeV] state is detected, the isovector spin-transfer selectivity is obtained. High-purity germanium clover detectors served to detect the gamma rays. Doppler reconstruction was used to determine the gamma energy in the rest frame of Li-6. From the Li-6 and 3.56 MeV gamma-momentum vectors the excitation energy of the residual nucleus was determined. Results: In the study of the C-12(Li-6,Li-6*[3.56 MeV]) reaction, the isovector spin-transfer excitation-energy spectrum in the inelastic channel was successfully measured. The strong Gamow-Teller state in C-12 at 15.1 MeV was observed. Comparisons with the analog C-12(Li-6,He-6) reaction validate the method of extracting the Gamow-Teller strength. In measurements of the Mg-24, Nb-93(Li-6,Li-6*[3.56 MeV]) reactions, the 3.56 MeV gamma peak could not be isolated from the strong background in the gamma spectrum from the decay of the isoscalar excitations. It is argued that by using a gamma-ray tracking array instead of a clover array, it is feasible to extend the mass range over which the (Li-6,Li-6*) reaction can be used for extracting the isovector spin-transfer response up to mass numbers of similar to 25 and perhaps higher. Conclusions: It is demonstrated that the (Li-6,Li-6*[3.56 MeV]) reaction probe can be used to isolate the inelastic isovector spin-transfer response in nuclei. Application to nuclei with mass numbers of about 25 or more, however, will require a more efficient gamma-ray array with a better tracking capability.