Spins and magnetic moments of ${}^{58,60,62,64}\mathrm{Mn}$ ground states and isomers

The odd-odd ${}^{54,56,58,60,62,64}\mathrm{Mn}$ isotopes ($Z=25$) were studied using bunched-beam collinear laser spectroscopy at ISOLDE, CERN. From the measured hyperfine spectra the spins and magnetic moments of Mn isotopes up to $N=39$ were extracted. The previous tentative ground state spin assignments of ${}^{58,60,62,64}\mathrm{Mn}$ are now firmly determined to be $I=1$ along with an $I=4$ assignment for the isomeric states in ${}^{58,60,62}\mathrm{Mn}$. The $I=1$ magnetic moments show a decreasing trend with increasing neutron number while the $I=4$ moments remain quite constant between $N=33$ and $N=37$. The results are compared to large-scale shell-model calculations using the GXPF1A and LNPS effective interactions. The excellent agreement of the ground state moments with the predictions from the LNPS calculations illustrates the need for an increasing amount of proton excitations across $Z=28$ and neutron excitations across $N=40$ in the ground state wave functions from $N=37$ onwards.

Figure 1

Hyperfine spectra of ${}^{62}\mathrm{Mn}$ taken without (shaded spectrum) and with (plain spectrum) proton gating. With proton gating photons are accepted only during one half-life of the shortest-lived isomer after proton impact. This clearly enhances the hyperfine structure of the short-lived state (indicated with arrows) with respect to the long-lived state. For visual comparison, the nongated spectrum is scaled to match the background intensity. The frequency is shown relative to the ${}^6{S}_{5/2}\to {}^6{P}_{3/2}$ literature transition frequency of ${}^{55}\mathrm{Mn}$ [23].

Figure 2

Hyperfine spectra of the ${}^{58,60,62,64}\mathrm{Mn}{1}^{+}$ states (blue) and ${}^{58,60,62}\mathrm{Mn}{4}^{+}$ states (red) obtained by bunched-beam collinear laser spectroscopy on the atomic ${}^6{S}_{5/2}\to {}^6{P}_{3/2}$ line. For ${}^{60,62,64}\mathrm{Mn}$ proton gating was used. The inset shows a schematic depiction of the hyperfine structure of an $I=1$ state along with the allowed hyperfine transitions. The frequency is shown relative to the ${}^6{S}_{5/2}\to {}^6{P}_{3/2}$ literature centroid of ${}^{55}\mathrm{Mn}$ [23].

Figure 3

Extracted quadrupole moments assuming different spins for the low-spin state and high-spin state in ${}^{58,60,62,64}\mathrm{Mn}$. Note that the error bars are in most cases smaller than the symbols on this scale. These are compared with the known literature quadrupole moments. The shaded area represents the minimum and maximum literature value in the Mn chain.

Figure 4

The single-particle orbitals and their parity relevant in the discussion of neutron-rich Mn isotopes. In a simple shell-model picture the five valence protons reside in $\pi f_{7/2}$ and the valence neutrons occupy the $pf$ orbitals.

Figure 5

${}^{58,60,62,64}\mathrm{Mn}$ energy levels below 1 MeV compared to GXPF1A and LNPS calculations. The long-lived $1^{+}$ and $4^{+}$ states are highlighted with a bold line. Experimental levels taken from the most recent Nuclear Data Sheets [28, 29, 30, 31] and [17, 44].

Figure 6

${}^{58,60,62,64}\mathrm{Mn}g$ factors of the $1^{+}$ (a) and $4^{+}$ states (b). Comparison of experimental values with shell-model calculations performed with GXPF1A (dashed line) and LNPS (dotted line).

Figure 7

Neutron (a) and proton (b) occupation numbers of the $1^{+}$ state calculated with the LNPS effective interaction. There is a large similarity between the odd-even Mn (shaded) and odd-odd Mn (solid) occupations.