High-resolution study of Gamow-Teller excitations in the $^{42}\mathrm{Ca}(^{3}\mathrm{He},t)\phantom{\rule{0.28em}{0ex}}^{42}\mathrm{Sc}$ reaction and the observation of a ``low-energy super-Gamow-Teller state''

High-resolution study of Gamow-Teller excitations in the ${}^{42}{Ca} ({}^{3}{He}, t) {}^{42}{Sc}$ reaction and the observation of a “low-energy super-Gamow-Teller state”

Y. Fujita et al.

Phys. Rev. C 91, 064316 – Published 26 June 2015

Abstract

To study the Gamow-Teller (GT) transitions from the $T_{z} = + 1$ nucleus ${}^{42}{Ca}$ to the $T_{z} = 0$ nucleus ${}^{42}{Sc}$ , where $T_{z}$ is the $z$ component of isospin $T$ , we performed a ( $p, n$ )-type $({}^{3}{He}, t)$ charge-exchange reaction at 140 MeV/nucleon and scattering angles around $0^{\circ}$ . With an energy resolution of 29 keV, states excited by GT transitions (GT states) could be studied accurately. The reduced GT transition strengths $B (GT)$ were derived up to the excitation energy of 13 MeV, assuming the proportionality between the cross sections at $0^{\circ}$ and $B (GT)$ values. The main part of the observed GT transition strength is concentrated in the lowest 0.611-MeV, $J^{π} = 1^{+}$ GT state. All the other states at higher energies are weakly excited. Shell-model calculations could reproduce the gross feature of the experimental $B (GT)$ distribution, and random-phase-approximation calculations including an attractive isoscalar interaction showed that the 0.611-MeV state has a collective nature. It was found that this state has all of the properties of a “low-energy super-Gamow-Teller state.” It is expected that low-lying $J^{π} = 1^{+}$ GT states have $T = 0$ in the $T_{z} = 0$ nucleus ${}^{42}{Sc}$ . However, $T = 1$ states are situated in a higher energy region. Assuming an isospin-analogous structure in $A = 42$ isobars, analogous $T = 1, 1^{+}$ states are also expected in ${}^{42}{Ca}$ . Comparing the ${}^{42}{Ca} ({}^{3}{He}, t) {}^{42}{Sc}$ and ${}^{42}{Ca} (p, p^{'})$ spectra measured at $0^{\circ}$ , candidates for $T = 1$ GT states could be found in the $10 - 12 - MeV$ region of ${}^{42}{Sc}$ . They were all weakly excited. The mass dependence of the GT strength distributions in Sc isotopes is also discussed.

Received 14 January 2015
Revised 20 May 2015

DOI:https://doi.org/10.1103/PhysRevC.91.064316

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Vol. 91, Iss. 6 — June 2015

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Figure 1
The $0^{\circ}, {}^{42}{Ca} ({}^{3}{He}, t) {}^{42}{Sc}$ spectrum on two scales. The events within the range of scattering angles $Θ \leq 0 . 5^{\circ}$ are included. (a) The full count range spectrum. Two prominent peaks are observed in the low-energy region and less prominent ones up to 4 MeV. (b) The vertical scale is magnified by a factor of 24. A fine structure of many states is observed up to $E_{x} = 12.7$ MeV. Major states populated in $Δ L = 0$ transitions ( $Δ L = 0$ states) below 7 MeV are indicated by their excitation energies in MeV. The $Δ L = 0$ states in the region above 7 MeV are indicated in Fig. 5 in Sec. 4.
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Figure 2
Angular distributions of $Δ L = 0$ and $Δ L \geq 1$ states observed in the low- $E_{x}$ region of the ( ${}^{3}{He}, t$ ) measurements. The $E_{x}$ values and $J^{π}$ values are from Ref. [34]. The vertical scale shows the counts of individual states in the spectrum of the $Θ \leq 0 . 5^{\circ}$ cut. They are shown as “Counts ( $0^{\circ}$ )” in Table 1. The counts in the spectra with larger angle cuts are corrected by the ratios of the solid angles.
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Figure 3
Schematic view of the analog states (connected by dashed lines) and analogous transitions in the mass $A = 42, T_{z} = + 1$ , 0, and $- 1$ isobaric system. The Coulomb displacement energies are removed so that the isospin symmetry becomes clear. In this scheme, the inclined arrows show the $0^{+} \to 1^{+}$ GT transitions caused by the $σ τ$ -type operator from the g.s.s of mirror nuclei ${}^{42}{Ca}$ and ${}^{42}{Ti}$ . However, the analogous $0^{+} \to 0^{+}$ Fermi transitions to the IAS caused by the $τ$ -type operator are shown by the horizontal arrows. The vertical arrows show the $0^{+} \to 1^{+}$ transitions caused by inelastic-type reactions such as ( $p, p^{'}$ ) or ( $e, e^{'}$ ) on ${}^{42}{Ca}$ .
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Figure 4
A comparison of the cumulative sums (CSs) of $B (GT)$ strengths from the experimental ${}^{42}{Ca} ({}^{3}{He}, t) {}^{42}{Sc}$ measurement and the SM calculation using the effective interaction GXPF1J. A quenching factor of ${(0.74)}^{2}$ is included in the SM calculation.
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Figure 5
(a) The ${}^{42}{Ca} ({}^{3}{He}, t)$ spectrum of the $E_{x} = 6.5 - 12.5$ -MeV region for events with scattering angles $Θ \leq 0 . 5^{\circ}$ . The counts of the continuum caused by the quasifree scattering (QFS) increase, in particular, in the $E_{x} = 8 - 11$ -MeV region. States with or probably with $Δ L = 0$ are indicated by their excitation energies. States originated from ${}^{40}{Ca}, {}^{16}O$ , and ${}^{12}C$ contaminants in the ${}^{42}{Ca}$ target are also indicated. (b) The IUCF ${}^{42}{Ca} (p, p^{'})$ spectrum measured at $E_{p} = 200$ MeV [59]. The measurements were carried out at very forward angles including $0^{\circ}$ using the K600 spectrometer in transmission mode [64]. The $E_{x} > 8.5$ -MeV region in ${}^{42}{Ca}$ was studied. The peaks corresponding to the $Δ L = 0$ states in the ( ${}^{3}{He}, t$ ) spectrum are shown by arrows. The vertical scales are adjusted so that the 10.011-MeV state in the ( ${}^{3}{He}, t$ ) spectrum and the corresponding state in the ( $p, p^{'}$ ) spectrum have nearly the same heights. Note that the ordinate of the ${}^{42}{Ca} (p, p^{'})$ spectrum begins with a finite count to illustrate the structured part clearly.
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Figure 6
The SM configurations before and after the $β^{-}$ -type GT transitions in $A = 42 - 48$ Ca isotopes. Positions occupied by neutrons ( $ν$ ) are shown by open crosses. Positions that are newly occupied by protons and unoccupied by neutrons after making GT transitions (shown by the arrows) are indicated by solid crosses and open circles, respectively. The shell closures at $Z = N = 20$ and 28 are indicated by thick solid lines.
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Physical Review C

covering nuclear physics

High-resolution study of Gamow-Teller excitations in the ${}^{42}{Ca} ({}^{3}{He}, t) {}^{42}{Sc}$ reaction and the observation of a “low-energy super-Gamow-Teller state”

Y. Fujita et al.

Phys. Rev. C 91, 064316 – Published 26 June 2015

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Physical Review C

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High-resolution study of Gamow-Teller excitations in the Ca42(He3,t)Sc42 reaction and the observation of a “low-energy super-Gamow-Teller state”

Y. Fujita et al.

Phys. Rev. C 91, 064316 – Published 26 June 2015

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High-resolution study of Gamow-Teller excitations in the ${}^{42}{Ca} ({}^{3}{He}, t) {}^{42}{Sc}$ reaction and the observation of a “low-energy super-Gamow-Teller state”