JUN45 Shell-Model Interaction Overview

• JUN45 Interaction is an effective shell-model Hamiltonian for the f5/2-p-g9/2 valence space above a 56Ni core, calibrated with around 400 experimental data points.
• It accurately predicts energy spectra, electromagnetic observables, and β-decay rates in the mass region A=63–96, serving as a benchmark for nuclear structure studies.
• The interaction’s success in spectroscopy is balanced by limitations in deformation-sensitive observables, motivating extensions like JUN45+LNPS and enlarged model spaces.

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 (Kumar et al., 2023, Obaid et al., 2022).

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” (Kumar et al., 2023). In practical shell-model work, the interaction is ordinarily used for valence nucleons outside a $^{56}$Ni core in the four-orbit space

$^{56}$0

which several applications denote as the $^{56}$1 space or, in NuShellX@MSU, as the “jj44” space (Obaid et al., 2022).

The intended region of applicability is the medium-mass sector where the $^{56}$2 intruder orbital becomes important, especially near $^{56}$3 and toward $^{56}$4. 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 $^{56}$5 and $^{56}$6 (Kumar et al., 2015, Hirsch et al., 2012).

A related but distinct construct is JUN45+LNPS. In the $^{56}$7, $^{56}$8 triplet study, this extended interaction keeps JUN45 in the original four-orbit space and supplements it with LNPS matrix elements involving the added $^{56}$9 orbital (Lenzi et al., 2021). 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,

$A=63\text{–}96$0

or an equivalent $A=63\text{–}96$1-coupled form in shell-model codes (Kumar et al., 2023, Kumar et al., 2015). The single-particle energies quoted repeatedly for JUN45 are

$A=63\text{–}96$2

$A=63\text{–}96$3

(Kumar et al., 2023). In a PHFB application to $A=63\text{–}96$4Ge and $A=63\text{–}96$5Se, an HFB2 implementation based on JUN45 used the set $A=63\text{–}96$6, $A=63\text{–}96$7, $A=63\text{–}96$8, and $A=63\text{–}96$9 MeV, which is specific to that calculation rather than the standard quoted shell-model parametrization (Rath et al., 2017).

Many studies use the full $N=50$0 space without additional truncation. That is stated explicitly for shell-model calculations of $N=50$1/EC decay, inelastic electron scattering, odd-$N=50$2 As isotopes, and high-spin $N=50$3Sr and $N=50$4Zr (Kumar et al., 2023, Obaid et al., 2022, Kumar et al., 2015, Srivastava et al., 2016). The main diagonalization environments are NuShellX@MSU and ANTOINE (Kumar et al., 2023, Kumar et al., 2015).

JUN45 does not fix a unique set of effective operators. For $N=50$5 observables, studies commonly adopt

$N=50$6

or, in some applications,

$N=50$7

(Kumar et al., 2015, Hirsch et al., 2012). In the $N=50$8 triplet, the comparison was instead between Dufour–Zuker charges,

$N=50$9

and standard charges,

$\beta$0

(Lenzi et al., 2021). Magnetic moments are often computed with

$\beta$1

while keeping orbital $\beta$2 at their usual values (Kumar et al., 2015, Srivastava et al., 2016, Kanellakopoulos et al., 2020).

A common misconception is that these charges or $\beta$3-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-$\beta$4 arsenic isotopes $\beta$5As, 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 (Kumar et al., 2015). In $\beta$6As, this includes the correct $\beta$7 ground state, whereas jj44b predicts $\beta$8 (Kumar et al., 2015).

For $\beta$9Sr and $\beta$0Zr, both JUN45 and jj44b reproduce much of the observed high-spin structure, but JUN45 gives especially good low-lying negative-parity states in $\beta$1Sr and reproduces the measured $\beta$2 and $\beta$3 values better than jj44b in both nuclei (Srivastava et al., 2016). The same study identifies the dominant structural motifs: one neutron hole in $\beta$4 for $\beta$5Sr and three neutron holes in $\beta$6 for low-lying positive-parity states in $\beta$7Zr (Srivastava et al., 2016).

In germanium, the picture is more differentiated. A comprehensive Ge-isotope study reports that JUN45 gives a good description of low-energy spectra in $\beta$8Ge and $\beta$9Ge, and it is the only interaction among JUN45, jj44b, and $f_{5/2}pg_{9/2}$0 that reproduces the anomalous feature that $f_{5/2}pg_{9/2}$1Ge has $f_{5/2}pg_{9/2}$2 as its first excited state (Hirsch et al., 2012). A separate Ge study found that JUN45 reproduces excitation energies very well, with an average absolute deviation of $f_{5/2}pg_{9/2}$3 MeV for $f_{5/2}pg_{9/2}$4Ge, but it performs poorly for static quadrupole moments of the $f_{5/2}pg_{9/2}$5 states (Robinson et al., 2010). This combination of strong spectroscopic performance and weak $f_{5/2}pg_{9/2}$6 performance recurs elsewhere in the JUN45 literature.

In selenium, JUN45 often gives reasonable spectra in the standard four-orbit space. For odd $f_{5/2}pg_{9/2}$7Se, it gives a particularly good account of $f_{5/2}pg_{9/2}$8Se and $f_{5/2}pg_{9/2}$9Se, but in $A=63-96$0Se the measured $A=63-96$1 level at $A=63-96$2 keV is predicted at $A=63-96$3 keV, which the authors interpret as evidence that the $A=63-96$4 orbital becomes necessary near $A=63-96$5 (Kumar et al., 2013).

For odd Ga isotopes $A=63-96$6Ga, JUN45 captures some broad trends, including the onset of intruder $A=63-96$7 structure, but the comparative verdict is less favorable: “for lighter isotopes $A=63-96$8 interaction is better and for heavier isotopes jj44b is quantitatively better than JUN45” (Srivastava, 2011). 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=63-96$9, $N=50$0 triplet $N=50$1Kr–$N=50$2Br–$N=50$3Se, JUN45 plus Coulomb gives

$N=50$4

for $N=50$5Kr, $N=50$6Br, and $N=50$7Se, with Coulomb-induced corrections of $N=50$8, $N=50$9, and $^{56}$0 efm$^{56}$1, respectively (Lenzi et al., 2021). It also gives

$^{56}$2

to be compared with experimental values $^{56}$3 keV and $^{56}$4 keV (Lenzi et al., 2021). With Dufour–Zuker effective charges, the calculations are described as compatible with the data; with standard charges, the apparent anomaly shifts from $^{56}$5Kr to $^{56}$6Br, and the study argues that a missing $^{56}$7, $^{56}$8 state in $^{56}$9Br is a plausible explanation (Lenzi et al., 2021). 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 $^{56}$00Cu and $^{56}$01Ga, JUN45 provides the shell-model wave functions in the jj44 space, while Sk35–Skzs$^{56}$02 residual correlations and core-polarization corrections are added through Tassie and Bohr–Mottelson prescriptions (Obaid et al., 2022). For $^{56}$03Cu, the resulting longitudinal and transverse form factors are in good agreement with experiment; for $^{56}$04Ga, the study concludes that effective charges are “not enough” and that “a microscopic theory should be used” (Obaid et al., 2022). 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 $^{56}$05 supply another precise benchmark. Using JUN45, the calculated ground-state moments are

$^{56}$06

$^{56}$07

to be compared with the measured values $^{56}$08, $^{56}$09 b, $^{56}$10, and $^{56}$11 b (Kanellakopoulos et al., 2020). The same work emphasizes that the $^{56}$12-factors lie close to effective single-particle values even though the JUN45 wave functions are “rather mixed” (Kanellakopoulos et al., 2020). 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: $^{56}$13 decay and double-$^{56}$14 decay

JUN45 has been used extensively for Gamow–Teller-driven decay in the Ni–Cu–Zn region. For $^{56}$15/EC decay of $^{56}$16 nuclei, it is used specifically for Ni, Cu, and Zn isotopes in the $^{56}$17 space, with shell-model calculations performed in NuShellX@MSU and with no additional truncations beyond the valence space (Kumar et al., 2023). That study extracted a GT quenching factor

$^{56}$18

for the full data set and

$^{56}$19

after excluding eight outlying points (Kumar et al., 2023). It further notes that the larger value gives half-lives “in general closer to the experiment.” Typical examples include $^{56}$20Cu $^{56}$21 $^{56}$22Ni, where JUN45 gives $^{56}$23 ms or $^{56}$24 ms against an experimental $^{56}$25 ms, and $^{56}$26Ni $^{56}$27 $^{56}$28Co, where it gives $^{56}$29 h or $^{56}$30 h against $^{56}$31 h (Kumar et al., 2023).

For $^{56}$32 decay in the same region, JUN45 is again used for Ni, Cu, and Zn, but the quenching extracted there is

$^{56}$33

in the $^{56}$34 space (Kumar et al., 2016). Near stability, the interaction can be highly accurate, as in $^{56}$35Ni with a calculated half-life of $^{56}$36 s against $^{56}$37 s, but toward $^{56}$38 it strongly underestimates half-lives: for $^{56}$39Ni it gives $^{56}$40 ms against $^{56}$41 ms (Kumar et al., 2016). 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 $^{56}$42 decay study sharpened the role of the $^{56}$43 orbital within JUN45. Using $^{56}$44, it found that for $^{56}$45Kr $^{56}$46 $^{56}$47Br, the yrast $^{56}$48 GT strength is enhanced relative to $^{56}$49Ge $^{56}$50 $^{56}$51Ga because of increased $^{56}$52 contribution, whereas in lighter systems such as $^{56}$53Zn the $^{56}$54 orbital has negligible effect and the missing $^{56}$55 correlations become more important (Choudhary et al., 15 Jul 2025). The same study explicitly rejects the blanket claim that stronger isoscalar $^{56}$56 pairing always enhances the lowest-state GT strength, while noting that accumulated GT strength generally increases when $^{56}$57 pairing matrix elements are strengthened (Choudhary et al., 15 Jul 2025).

JUN45 also enters double-$^{56}$58 decay work. In large-scale shell-model calculations of $^{56}$59 decay for $^{56}$60Se, JUN45 yields

$^{56}$61

using $^{56}$62 intermediate $^{56}$63 states in $^{56}$64Br up to $^{56}$65 MeV (Patel et al., 2023). With $^{56}$66, this gives

$^{56}$67

to be compared with the experimental average $^{56}$68 yr (Patel et al., 2023). The lowest $^{56}$69 state contributes $^{56}$70, or $^{56}$71 of the total NME, and the cumulative sum is described as essentially saturated by about $^{56}$72 MeV (Patel et al., 2023).

In a PHFB study of $^{56}$73 decay for $^{56}$74Ge and $^{56}$75Se, JUN45 serves as the empirical interaction whose TBMEs are spin–tensor decomposed into central, spin-orbit, and tensor parts (Rath et al., 2017). 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 $^{56}$76 for $^{56}$77 and $^{56}$78 for $^{56}$79 (Rath et al., 2017).

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 $^{56}$80 orbital as the main reason why lighter Se, Ga, and some Ge nuclei are undercollective in JUN45-based calculations (Srivastava et al., 2013, Srivastava, 2011, Srivastava et al., 2012). In even-even Se isotopes, for example, $^{56}$81 calculations with proton $^{56}$82 reproduce the large $^{56}$83 values in $^{56}$84Se much better than JUN45, leading the authors to conclude that “proton excitation across $^{56}$85 shell for lighter Se isotopes are important” (Srivastava et al., 2013).

Near $^{56}$86, missing $^{56}$87 degrees of freedom are repeatedly invoked. In odd Se isotopes, the $^{56}$88Se $^{56}$89 level is predicted far too high in JUN45, and the authors explicitly state that “it is now important to include $^{56}$90 orbital” as $^{56}$91 is approached (Kumar et al., 2013). The same conclusion appears in arsenic work, which calls for enlarging the space to include both $^{56}$92 and $^{56}$93 (Kumar et al., 2015).

A second recurrent issue is that agreement in excitation energies does not imply agreement in deformation-sensitive observables. In $^{56}$94Ge, JUN45 gives excellent excitation energies but predicts

$^{56}$95

for $^{56}$96Ge, whereas the measured values are $^{56}$97, $^{56}$98, and $^{56}$99 fm$A=63\text{–}96$00, respectively (Robinson et al., 2010). 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 $A=63\text{–}96$01 in Ge, JUN45 reproduces several $A=63\text{–}96$02-factors that lie close to effective single-particle values, but the same calculations show strongly mixed wave functions (Kanellakopoulos et al., 2020). 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 $A=63\text{–}96$03 and allows up to $A=63\text{–}96$04 excitations from $A=63\text{–}96$05 and $A=63\text{–}96$06 to the $A=63\text{–}96$07 shells, with $A=63\text{–}96$08 from $A=63\text{–}96$09, and improves the spectroscopy of the $A=63\text{–}96$10 triplet while leaving the basic $A=63\text{–}96$11 pattern close to the original JUN45 result (Lenzi et al., 2021). Enlarged $A=63\text{–}96$12 spaces that restore $A=63\text{–}96$13 likewise improve quadrupole moments, $A=63\text{–}96$14 values, and some magnetic moments in Ga, Se, and Ge (Srivastava, 2011, Srivastava et al., 2012).

Taken together, these studies define JUN45 as a technically mature and regionally successful interaction for the $A=63\text{–}96$15Ni-based $A=63\text{–}96$16 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 $A=63\text{–}96$17, neutron excitations toward $A=63\text{–}96$18 near $A=63\text{–}96$19, and deformation-sensitive observables can require larger spaces or hybrid extensions beyond the canonical JUN45 Hamiltonian (Hirsch et al., 2012, Kumar et al., 2013).