---
title: JUN45 Shell-Model Interaction Overview
url: https://www.emergentmind.com/topics/jun45-interaction
type: topic
---

# JUN45 Shell-Model Interaction Overview

Searching arXiv for recent and foundational papers on JUN45 and its applications.
JUN45 is a shell-model effective interaction for the \(f_{5/2}pg_{9/2}\) valence space above a \(^{56}\)Ni core, built from a realistic Bonn-C starting point and then empirically refined for nuclei in the mass region \(A=63\text{–}96\), with particular emphasis on data around the \(N=50\) shell closure. In the literature surveyed here, it functions as a standard Hamiltonian for spectroscopy, electromagnetic observables, \(\beta\)-decay, and double-\(\beta\) decay in nuclei from the Ni region to the Se–Zr region, while also serving as a baseline against which larger valence spaces and alternative interactions are judged [2310.01116][2206.09297].

## 1. Origin, scope, and nomenclature

Honma et al. developed JUN45 for the \(f_{5/2}pg_{9/2}\) model space. It is described as “a realistic interaction that is based on Bonn-C potential” and “fitted by 400 experimental data (binding and excitation energies) with mass numbers \(A=63-96\),” with many of those data taken “around \(N=50\) shell closure” [2310.01116]. In practical shell-model work, the interaction is ordinarily used for valence nucleons outside a \(^{56}\)Ni core in the four-orbit space
\[
1p_{3/2},\ 0f_{5/2},\ 1p_{1/2},\ 0g_{9/2},
\]
which several applications denote as the \(f_{5/2}pg_{9/2}\) space or, in NuShellX@MSU, as the “jj44” space [2206.09297].

The intended region of applicability is the medium-mass sector where the \(g_{9/2}\) intruder orbital becomes important, especially near \(N=40\) and toward \(N=50\). In that role, JUN45 is routinely contrasted with interactions defined in the same space, such as jj44b, and with enlarged spaces that add missing orbitals, most commonly \(\pi f_{7/2}\) and \(\nu d_{5/2}\) [1503.03219][1204.2845].

A related but distinct construct is JUN45+LNPS. In the \(A=70\), \(T=1\) triplet study, this extended interaction keeps JUN45 in the original four-orbit space and supplements it with LNPS matrix elements involving the added \(1d_{5/2}\) orbital [2106.10269]. That extension is not a redefinition of JUN45 itself; it is an enlarged-space hybrid built to test sensitivity to intruder configurations.

## 2. Valence space, Hamiltonian, and effective operators

In standard implementations, JUN45 enters the shell-model Hamiltonian through its single-particle energies and two-body matrix elements,
\[
H = \sum_i \epsilon_i a_i^\dagger a_i + \frac12 \sum_{ij,kl} \langle ij|V|kl\rangle a_i^\dagger a_j^\dagger a_l a_k,
\]
or an equivalent \(JT\)-coupled form in shell-model codes [2310.01116][1503.03219]. The single-particle energies quoted repeatedly for JUN45 are
\[
\epsilon(p_{3/2})=-9.8280~\text{MeV},\quad
\epsilon(f_{5/2})=-8.7087~\text{MeV},
\]
\[
\epsilon(p_{1/2})=-7.8388~\text{MeV},\quad
\epsilon(g_{9/2})=-6.2617~\text{MeV}
\]
[2310.01116]. In a PHFB application to \(^{76}\)Ge and \(^{82}\)Se, an HFB2 implementation based on JUN45 used the set \(-9.828\), \(-9.048\), \(-8.7480\), and \(-6.828\) MeV, which is specific to that calculation rather than the standard quoted shell-model parametrization [1707.02135].

Many studies use the full \(f_{5/2}pg_{9/2}\) space without additional truncation. That is stated explicitly for shell-model calculations of \(\beta^+\)/EC decay, inelastic electron scattering, odd-\(A\) As isotopes, and high-spin \(^{87}\)Sr and \(^{87}\)Zr [2310.01116][2206.09297][1503.03219][1603.04354]. The main diagonalization environments are NuShellX@MSU and ANTOINE [2310.01116][1503.03219].

JUN45 does not fix a unique set of effective operators. For \(E2\) observables, studies commonly adopt
\[
e_p=1.5\,e,\qquad e_n=0.5\,e
\]
or, in some applications,
\[
e_p=1.5\,e,\qquad e_n=1.1\,e
\]
[1503.03219][1204.2845]. In the \(A=70\) triplet, the comparison was instead between Dufour–Zuker charges,
\[
q_\pi=1.31e,\qquad q_\nu=0.46e,
\]
and standard charges,
\[
q_\pi=1.5e,\qquad q_\nu=0.5e
\]
[2106.10269]. Magnetic moments are often computed with
\[
g_s^{\text{eff}}=0.7\,g_s^{\text{free}}
\]
while keeping orbital \(g_l\) at their usual values [1503.03219][1603.04354][2011.01659].

A common misconception is that these charges or \(g\)-factor renormalizations are intrinsic parts of JUN45. The literature instead treats them as observable-dependent supplements to the interaction.

## 3. Spectroscopic applications and regional performance

JUN45 performs well in several regions for low-lying and high-spin spectroscopy, but its success is not uniform. In odd-\(A\) arsenic isotopes \(^{77,79,81,83}\)As, the overall results for energy levels and magnetic moments are reported to be “in rather good agreement with the available experimental data,” and the authors conclude that “the results of JUN45 interaction is better than jj44b” in that chain [1503.03219]. In \(^{79}\)As, this includes the correct \(3/2^-\) ground state, whereas jj44b predicts \(1/2^-\) [1503.03219].

For \(^{87}\)Sr and \(^{87}\)Zr, both JUN45 and jj44b reproduce much of the observed high-spin structure, but JUN45 gives especially good low-lying negative-parity states in \(^{87}\)Sr and reproduces the measured \(Q(9/2_1^+)\) and \(\mu(9/2_1^+)\) values better than jj44b in both nuclei [1603.04354]. The same study identifies the dominant structural motifs: one neutron hole in \(\nu g_{9/2}\) for \(^{87}\)Sr and three neutron holes in \(\nu g_{9/2}\) for low-lying positive-parity states in \(^{87}\)Zr [1603.04354].

In germanium, the picture is more differentiated. A comprehensive Ge-isotope study reports that JUN45 gives a good description of low-energy spectra in \(^{70,72,74}\)Ge and \(^{80}\)Ge, and it is the only interaction among JUN45, jj44b, and \(fpg\) that reproduces the anomalous feature that \(^{72}\)Ge has \(0_2^+\) as its first excited state [1204.2845]. A separate Ge study found that JUN45 reproduces excitation energies very well, with an average absolute deviation of \(0.133\) MeV for \({}^{70,72,74,76}\)Ge, but it performs poorly for static quadrupole moments of the \(2_1^+\) states [1007.0264]. This combination of strong spectroscopic performance and weak \(Q_s\) performance recurs elsewhere in the JUN45 literature.

In selenium, JUN45 often gives reasonable spectra in the standard four-orbit space. For odd \(^{79,81,83}\)Se, it gives a particularly good account of \(^{79}\)Se and \(^{81}\)Se, but in \(^{83}\)Se the measured \(1/2^+\) level at \(360\) keV is predicted at \(1636\) keV, which the authors interpret as evidence that the \(\nu d_{5/2}\) orbital becomes necessary near \(N=50\) [1311.4060].

For odd Ga isotopes \(^{71-78}\)Ga, JUN45 captures some broad trends, including the onset of intruder \(9/2^+\) structure, but the comparative verdict is less favorable: “for lighter isotopes \(fpg\) interaction is better and for heavier isotopes jj44b is quantitatively better than JUN45” [1106.0571]. This suggests that JUN45 is often structurally informative in the Ga chain, but not the most accurate option available within the tested interactions.

## 4. Electromagnetic observables, moments, and form factors

Electromagnetic observables provide some of the sharpest tests of JUN45. In the \(A=70\), \(T=1\) triplet \(^{70}\)Kr–\(^{70}\)Br–\(^{70}\)Se, JUN45 plus Coulomb gives
\[
M_p(E2)=52.2,\ 47.0,\ 43.5~\text{efm}^2
\]
for \(^{70}\)Kr, \(^{70}\)Br, and \(^{70}\)Se, with Coulomb-induced corrections of \(+3.4\), \(+0.7\), and \(-0.3\) efm\(^2\), respectively [2106.10269]. It also gives
\[
\text{MED}=-100~\text{keV},\qquad \text{TED}=-17~\text{keV},
\]
to be compared with experimental values \(-67.0(7.5)\) keV and \(-45.2(7.5)\) keV [2106.10269]. With Dufour–Zuker effective charges, the calculations are described as compatible with the data; with standard charges, the apparent anomaly shifts from \(^{70}\)Kr to \(^{70}\)Br, and the study argues that a missing \(1^+\), \(T=0\) state in \(^{70}\)Br is a plausible explanation [2106.10269]. This suggests that some apparent “JUN45 failures” in E2 systematics are entangled with effective-charge choices and incomplete spectroscopy rather than the interaction alone.

In electron scattering from \(^{65}\)Cu and \(^{71}\)Ga, JUN45 provides the shell-model wave functions in the jj44 space, while Sk35–Skzs\(^*\) residual correlations and core-polarization corrections are added through Tassie and Bohr–Mottelson prescriptions [2206.09297]. For \(^{65}\)Cu, the resulting longitudinal and transverse form factors are in good agreement with experiment; for \(^{71}\)Ga, the study concludes that effective charges are “not enough” and that “a microscopic theory should be used” [2206.09297]. This is a concrete example in which JUN45-based valence-space structure is adequate in one nucleus and insufficient in another, even within the same formalism.

Magnetic and quadrupole moments of Ge isotopes around \(N=40\) supply another precise benchmark. Using JUN45, the calculated ground-state moments are
\[
\mu(^{69}\text{Ge})=+1.048~\mu_N,\qquad Q_s(^{69}\text{Ge})=+0.150~\text{b},
\]
\[
\mu(^{73}\text{Ge})=-0.955~\mu_N,\qquad Q_s(^{73}\text{Ge})=-0.258~\text{b},
\]
to be compared with the measured values \(+0.920(5)\,\mu_N\), \(+0.114(8)\) b, \(-0.904(21)\,\mu_N\), and \(-0.198(4)\) b [2011.01659]. The same work emphasizes that the \(g\)-factors lie close to effective single-particle values even though the JUN45 wave functions are “rather mixed” [2011.01659]. A plausible implication is that single-particle-like magnetic observables do not guarantee pure single-particle wave functions in the JUN45 basis.

## 5. Weak processes: \(\beta\) decay and double-\(\beta\) decay

JUN45 has been used extensively for Gamow–Teller-driven decay in the Ni–Cu–Zn region. For \(\beta^+\)/EC decay of \(Z=21\text{–}30\) nuclei, it is used specifically for Ni, Cu, and Zn isotopes in the \(f_{5/2}pg_{9/2}\) space, with shell-model calculations performed in NuShellX@MSU and with no additional truncations beyond the valence space [2310.01116]. That study extracted a GT quenching factor
\[
q=0.743\pm0.030
\]
for the full data set and
\[
q=0.768\pm0.030
\]
after excluding eight outlying points [2310.01116]. It further notes that the larger value gives half-lives “in general closer to the experiment.” Typical examples include \(^{57}\)Cu \(\to\) \(^{57}\)Ni, where JUN45 gives \(173.2\) ms or \(151.8\) ms against an experimental \(196.3\pm7\) ms, and \(^{57}\)Ni \(\to\) \(^{57}\)Co, where it gives \(32.8\) h or \(37.9\) h against \(35.60\pm0.06\) h [2310.01116].

For \(\beta^-\) decay in the same region, JUN45 is again used for Ni, Cu, and Zn, but the quenching extracted there is
\[
q=0.684\pm0.015
\]
in the \(f_{5/2}pg_{9/2}\) space [1603.03897]. Near stability, the interaction can be highly accurate, as in \(^{67}\)Ni with a calculated half-life of \(21.19\) s against \(21\pm1\) s, but toward \(N=50\) it strongly underestimates half-lives: for \(^{78}\)Ni it gives \(2.255\) ms against \(122.2\pm5.1\) ms [1603.03897]. This suggests that, in very neutron-rich nuclei, the standard JUN45 space places too much GT strength too low in the daughter spectrum.

A recent \(N=Z\) decay study sharpened the role of the \(g_{9/2}\) orbital within JUN45. Using \(q=0.79\), it found that for \(^{70}\)Kr \(\to\) \(^{70}\)Br, the yrast \(1^+\) GT strength is enhanced relative to \(^{62}\)Ge \(\to\) \(^{62}\)Ga because of increased \(g_{9/2}\) contribution, whereas in lighter systems such as \(^{58}\)Zn the \(g_{9/2}\) orbital has negligible effect and the missing \(f_{7/2}\) correlations become more important [2507.11769]. The same study explicitly rejects the blanket claim that stronger isoscalar \(np\) pairing always enhances the lowest-state GT strength, while noting that accumulated GT strength generally increases when \(T=0\) pairing matrix elements are strengthened [2507.11769].

JUN45 also enters double-\(\beta\) decay work. In large-scale shell-model calculations of \(2\nu\beta\beta\) decay for \(^{82}\)Se, JUN45 yields
\[
|M_{2\nu}|=0.1713,
\]
using \(5000\) intermediate \(1^+\) states in \(^{82}\)Br up to \(24.874\) MeV [2310.19015]. With \(g_A^{\text{eff}}=0.76\), this gives
\[
t_{1/2}^{2\nu}=0.68\times10^{20}\ \text{yr},
\]
to be compared with the experimental average \(0.87^{+0.02}_{-0.01}\times10^{20}\) yr [2310.19015]. The lowest \(1^+\) state contributes \(0.0557\), or \(32.5\%\) of the total NME, and the cumulative sum is described as essentially saturated by about \(7\) MeV [2310.19015].

In a PHFB study of \(0\nu\beta\beta\) decay for \(^{76}\)Ge and \(^{82}\)Se, JUN45 serves as the empirical interaction whose TBMEs are spin–tensor decomposed into central, spin-orbit, and tensor parts [1707.02135]. There the main conclusion is that the central part carries most of the SRC sensitivity, the spin-orbit part is important but not dominant, and the tensor part is comparatively small; the maximum uncertainty in the average NTMEs is reported to be about \(10\%\) for \(\overline{M}^{(0\nu)}\) and \(37\%\) for \(\overline{M}^{(0N)}\) [1707.02135].

## 6. Limitations, extensions, and recurrent interpretive issues

The most persistent limitation of JUN45 is not usually framed as a defect of its fitted TBMEs alone, but as a consequence of its restricted four-orbit valence space. Multiple studies identify the missing \(\pi f_{7/2}\) orbital as the main reason why lighter Se, Ga, and some Ge nuclei are undercollective in JUN45-based calculations [1304.5766][1106.0571][1210.5790]. In even-even Se isotopes, for example, \(fpg\) calculations with proton \(f_{7/2}\) reproduce the large \(B(E2;2_1^+\to 0_1^+)\) values in \(^{78,80}\)Se much better than JUN45, leading the authors to conclude that “proton excitation across \(Z=28\) shell for lighter Se isotopes are important” [1304.5766].

Near \(N=50\), missing \(\nu d_{5/2}\) degrees of freedom are repeatedly invoked. In odd Se isotopes, the \(^{83}\)Se \(1/2^+\) level is predicted far too high in JUN45, and the authors explicitly state that “it is now important to include \(\nu 1d_{5/2}\) orbital” as \(N=50\) is approached [1311.4060]. The same conclusion appears in arsenic work, which calls for enlarging the space to include both \(\pi 0f_{7/2}\) and \(\nu 1d_{5/2}\) [1503.03219].

A second recurrent issue is that agreement in excitation energies does not imply agreement in deformation-sensitive observables. In \({}^{70,72,74,76}\)Ge, JUN45 gives excellent excitation energies but predicts
\[
Q(2_1^+) = +12.85,\ +12.02,\ +1.77~\text{fm}^2
\]
for \(^{72,74,76}\)Ge, whereas the measured values are \(-13(6)\), \(-25(6)\), and \(-19(6)\) fm\(^2\), respectively [1007.0264]. That sign reversal is one of the clearest examples in the literature of JUN45 reproducing the spectrum but not the intrinsic quadrupole character.

A third interpretive issue concerns apparently single-particle observables. Around \(N=40\) in Ge, JUN45 reproduces several \(g\)-factors that lie close to effective single-particle values, but the same calculations show strongly mixed wave functions [2011.01659]. This argues against identifying single-particle-like moments with weak configuration mixing.

Extensions built on JUN45 are designed precisely to address these limitations. JUN45+LNPS adds \(1d_{5/2}\) and allows up to \(10p\text{–}10h\) excitations from \(p_{1/2}\) and \(f_{5/2}\) to the \(gd\) shells, with \(4p\text{–}4h\) from \(p_{3/2}\), and improves the spectroscopy of the \(A=70\) triplet while leaving the basic \(E2\) pattern close to the original JUN45 result [2106.10269]. Enlarged \(fpg\) spaces that restore \(\pi f_{7/2}\) likewise improve quadrupole moments, \(B(E2)\) values, and some magnetic moments in Ga, Se, and Ge [1106.0571][1210.5790].

Taken together, these studies define JUN45 as a technically mature and regionally successful interaction for the \(^{56}\)Ni-based \(f_{5/2}pg_{9/2}\) shell, especially for spectra, many GT observables, and selected moments. They also show that its predictive limits are systematic rather than anecdotal: collectivity driven by proton cross-shell excitations across \(Z=28\), neutron excitations toward \(d_{5/2}\) near \(N=50\), and deformation-sensitive observables can require larger spaces or hybrid extensions beyond the canonical JUN45 Hamiltonian [1204.2845][1311.4060].

Source: https://www.emergentmind.com/topics/jun45-interaction