Neutron effective single-particle energies above ${}^{78}\mathrm{Ni}$: A hint from lifetime measurements in the $N=51$ isotones ${}^{85}\mathrm{Se}$ and ${}^{87}\mathrm{Kr}$

Background: While the $N=50$ shell-gap evolution towards ${}^{78}\mathrm{Ni}$ is presently in the focus of nuclear structure research, experimental information on the neutron effective single-particle energy sequence above the ${}^{78}\mathrm{Ni}$ core remain scarce. Direct nucleon-exchange reactions are indeed difficult with presently available post-accelerated radioactive-ion beams (especially for high orbital-momentum orbitals) in this exotic region.

Purpose: In this study we probe the evolution of the $\nu 1g_{7/2}$ effective single-particle energy which is a key to understanding the possible evolution of the spin-orbit splitting due to the proton-neutron interaction in the ${}^{78}\mathrm{Ni}$ region. To achieve this goal, a method based on lifetime measurements is used for the first time. The obtained lifetimes of the $7/2_1^{+}$ states in ${}^{87}\mathrm{Kr}$ and ${}^{85}\mathrm{Se}$ are used to investigate the $\nu 1g_{7/2}$ evolution.

Method: Yrast and near-yrast states in the light $N=51$ isotones ${}^{85}\mathrm{Se}$ and ${}^{87}\mathrm{Kr}$ were populated via multinucleon transfer reactions, using a ${}^{82}\mathrm{Se}$ beam and a ${}^{238}\mathrm{U}$ target at the LNL tandem-ALPI facility. The prompt $\gamma$ rays were detected by the AGATA Demonstrator and particle identification was performed using the PRISMA spectrometer. Lifetime measurements were performed by using the Cologne plunger device for deep inelastic reactions and the Recoil Distance Doppler Shift technique.

Results: We obtain ${\tau }_{(7/2_1^{+})}=0.4_{-0.4}^{+1.6}$ ps for ${}^{87}\mathrm{Kr}$. In the case of ${}^{85}\mathrm{Se}$ an upper limit of 3(2) ps is obtained for the ${\tau }_{7/2_1^{+}}$ value.

Conclusion: For ${}^{87}\mathrm{Kr}$, the measured $(7/2_1^{+})$ lifetime is consistent with a core-coupled $2^{+}\otimes \nu 2d_{5/2}$ configuration for this state. This result is consistent with that obtained by direct reaction, which validates our method. For ${}^{85}\mathrm{Se}$, the measured $7/2_1^{+}$ lifetime limit indicates a very small contribution of the $\nu 1g_{7/2}$ configuration to the wave function of this state.

Figure 1

Neutron single-particle energies above $N=50$. The opened and filled symbols indicates the Duflo–Zuker estimations [2] and recent shell-model calculations [3], respectively.

Figure 2

Mass spectra of Se (top) and Kr (bottom) isotopes for a charge state of $q=25+$.

Figure 3

(top panel) $\gamma$-ray spectrum in coincidence with ${}^{87}\mathrm{Kr}$ ions identified in PRISMA (blue histogram). The red curve corresponds to the $\gamma$ spectrum in coincidence with all nuclei except for Se ions identified in PRISMA. (bottom panel) ${}^{87}\mathrm{Kr}$ background-subtracted $\gamma$-ray spectrum.

Figure 4

Simplified decay network as assumed in the lifetime extraction procedure.

Figure 5

Schematic $R\left(\tau \right)$ curve that allows us to determine the level lifetime ${\tau }_i$.

Figure 6

$\gamma$-ray spectrum of ${}^{87}\mathrm{Kr}$ after background subtraction for a target-to-degrader distance of $38\mu \mathrm{m}$. The red curves correspond to Gaussian fits of the shifted and unshifted components of the $(7/2_1^{+})\to 5/2_{\text{gs}}^{+}$ and $9/2_1^{+}\to 5/2_{\text{gs}}^{+}$ transitions at 1420 and 1578 keV, respectively.

Figure 7

Variation of the effective lifetimes calculated from Eq. (1) as a function of the intensity ratio $R$. The blue and red curves correspond to the plunger distances of 38 and $257\mu \mathrm{m}$, respectively. The light blue and light red areas show the range of $R$ values observed in this work for transitions in ${}^{87}\mathrm{Kr}$ at 38 and $257\mu \mathrm{m}$, respectively.

Figure 8

$\gamma$-ray spectrum of ${}^{87}\mathrm{Kr}$ after background subtraction for a target-to-degrader distance of $257\mu \mathrm{m}$. The red curves correspond to Gaussian fits of the shifted and unshifted components of the (a) $(9/2_2^{+})\to (7/2_1^{+})$ transition at 422 keV, (b) $11/2_1^{-}\to 9/2_1^{+}$ transition at 681 keV, and the (c) $(7/2_1^{+})\to 5/2_{\text{gs}}^{+}$ and $9/2_1^{+}\to 5/2_{\text{gs}}^{+}$ transitions at 1420 and 1578 keV, respectively.

Figure 9

Level scheme of ${}^{87}\mathrm{Kr}$ as observed in the present work. Because the statistics was insufficient to obtain coincidence relationships, the spin assignments are from Ref. [36]. The dotted arrow represents the not-exploitable 911 keV transition.

Figure 10

Background-subtracted $\gamma$-ray spectra of ${}^{85}\mathrm{Se}$ for the target-to-degrader distances of (a), (b) $38\mu \mathrm{m}$ and (c), (d) $257\mu \mathrm{m}$. The red curves correspond to Gaussian fits of the shifted and unshifted components of (a), (c) the $7/2_1^{+}\to 5/2_{\text{gs}}^{+}$ and (b), (d) $(9/2_1^{+})\to 5/2_{\text{gs}}^{+}$ transitions at 1115 and 1436 keV, respectively. The dashed lines [panels (c) and (d)] show the location of the unshifted peak for the plunger distance of $257\mu \mathrm{m}$.

Figure 11

Effective lifetimes for the $7/2_1^{+}$ and $(9/2_1^{+})$ states in ${}^{85}\mathrm{Se}$ observed in this work. The level placement is from Refs. [18, 19, 21].

Figure 12

Systematics of some of the states of interest for the present discussion, for the light $N=51$ odd isotones from $Z=32$ to 42 (adapted from Ref. [9]). The evolution of the $2^{+}$ core-excited state in $N=50$ nuclei is also shown (green line). The $5/2^{+}$ ground states are shown in black, the $1/2^{+}$ and the $7/2^{+}$ states in blue and in red, respectively. The filled (open) circle symbols indicate the large (small) spectroscopic factors. The first $9/2+$ states are shown with purple square symbols.

Figure 13

Comparison between the core-coupling (middle column “CC”) and experimental (right column “EXPT”) level schemes for ${}^{89}\mathrm{Sr}$. The unperturbed energy of the core-coupled configurations are represented on the left column (“UNP”). Configurations expected in this energy region but not included in the calculations are with square brackets. Spectroscopic factors $S$ are written close to their associate levels, as well as some of the relevant lifetime values, $\tau$, given in ps. The experimental values for $S$ and $\tau$ were taken from Refs. [42] and [43], respectively (see also the full $A=89$ evaluation [41]).

Figure 14

Same as Fig. 13 but for ${}^{87}\mathrm{Kr}$ (experimental $S$ values are from Ref. [17]).

Figure 15

Same as Fig. 13 but for ${}^{85}\mathrm{Se}$ (experimental $S$ values are from Ref. [11]).