Collective properties of neutron-deficient Nd isotopes: Lifetime measurements of the yrast states in ${}^{136}\mathrm{Nd}$

Lifetimes of the low-energy levels in ${}^{136}\mathrm{Nd}$, populated in the reaction ${}^{124}\mathrm{Te}({}^{16}\mathrm{O},4n)$, were measured with the ROSPHERE array at the Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), Bucharest-Magurele. The data were analyzed using the recoil distance Doppler shift method, and, in the cases where lifetimes were $\tau ⩽1$ ps, Doppler attenuation effects were taken into account. The deduced electromagnetic transition probabilities are discussed in the framework of the five-dimensional collective Hamiltonian (5DCH) theoretical model implemented with the D1S Gogny force, and detailed systematics of several observables in the even-even Nd isotopic chain are presented that highlight the transitional character of the neutron-deficient Nd isotopes. The 5DCH predictions are in overall good agreement with the present experimental results.

Figure 1

Partial level scheme of ${}^{136}\mathrm{Nd}$ that highlights the levels of interest for this experiment, constructed using observed intensities, and mean lifetimes measured in this experiment.

Figure 2

Background subtracted spectra showing the peak intensity evolution of the $S$ component and $U$ component for $2_1^{+}\to 0^{+}$ (a), $4_1^{+}\to 2_1^{+}$ (b), $7_1^{-}\to 6_1^{+}$ (c), $9_1^{-}\to 7_1^{-}$ (d) transitions measured in the forward direction and ${14}_1^{+}\to {12}_1^{+}$ (e) in the backward direction. The transitions are obtained in coincidence with the $S$ component of the feeding $\gamma$ rays at 602.7, 886.0, 501.2, 661.2, and 844.3 keV, respectively.

Figure 3

Mean lifetimes for the $2_1^{+}$ (a), $4_1^{+}$ (c), $7_1^{-}$ (e), $9_1^{-}$ (i) states for each distance measured in the forward direction (${37}^{\circ }$) and for the ${14}_1^{+}$ (g) state measured in the backward direction (${143}^{\circ }$). The horizontal lines are the weighted averages of these values and their uncertainties. Normalized values of the $S$ component (black circles) and $U$ component (red squares) of the $2_1^{+}\to 0^{+}$ (b), $4_1^{+}\to 2_1^{+}$ (d), $7_1^{-}\to 6_1^{+}$ (f), $9_1^{-}\to 7_1^{-}$ (j) transition intensities measured in the forward direction and of the ${14}_1^{+}\to {12}_1^{+}$ (h) transition intensity measured in the backward direction.

Figure 4

Lifetime determination for the $6_1^{+}$ level in the yrast band of ${}^{136}\mathrm{Nd}$ using the gated spectra measured with the detectors at ${143}^{\circ }$ (left two groups of panels) and ${37}^{\circ }$ (right two groups of panels). The gate is set on the full line shape of the $\gamma$-ray transition of 603 keV on the bottom of the band (GFB). The first and third groups of panels present fits of the line shape of the 770 keV $\gamma$-ray transition at different distances. The solid black line is the full fit. The decomposition of the line shape into different components is also shown, with a subtracted constant and common number from the calculated spectra for more visibility. Namely, these are the unshifted peak and background (dashed blue line), the spectrum part generated by DSA effects (dotted red line), and the pure flight peak represented by a green long-dashed line. The second and fourth groups of panels illustrate the lifetime determination according to Eq. (8). On top, the derived $\tau$ curve is displayed with its uncertainties together with a fit with a horizontal line derived within the region of sensitivity. This curve is a result of the division of the numerator in that equation (middle panel) by the corresponding denominator (bottom panel). The mean lifetimes determined and their uncertainties are also shown. See also the main text.

Figure 5

Lifetime determination for the $8_1^{+}$ level in the yrast band of ${}^{136}\mathrm{Nd}$ using the gated spectra measured with the detectors at ${143}^{\circ }$ (left two groups of panels) and ${37}^{\circ }$ (right two groups of panels). The gate is set on the shifted component of the directly feeding transition of 920 keV observed with the detectors of the backward ring. The first and third groups of panels present fits of the line shape of the 886 keV $\gamma$-ray transition at different distances. The solid black line is the full fit. The second and fourth groups of panels illustrate the lifetime determination according to Eq. (9). On top, the derived $\tau$ curve is displayed together with a fit with a horizontal line derived within the region of sensitivity. See also the caption to Fig. 4 and the text.

Figure 6

Time delayed spectra corresponding to the lifetime of the $2_1^{+}$ state. The continuous line represents the convolution of the prompt response and the lifetime of the state. In the inset, the time difference between the centroids of the delayed (black histogram and red line) and the antidelayed (red histogram and black line) time distributions is shown.

Figure 7

Potential energy surfaces (MeV) over the ($\beta$, $\gamma$) collective coordinates for even-even mass Nd isotopes with neutron numbers from $N=70$ to $N=80$.

Figure 8

Mean $\beta$ and $\gamma$ deformations of Nd ground state levels over the $(\beta ,\gamma )$ plane. Mean deformations calculated for spin values up to $I=8$ form trajectories shown as continuous lines. The color code is intended to identify each trajectory.

Figure 9

Excitation energies (MeV) of ground state band levels up to spin $I=8\hslash$. The red and black circles are for experimental [48, 49, 50, 51, 52, 53] and calculated values, respectively.

Figure 10

Calculated ${\mathcal{J}}^{\left(1\right)}$ values (${\hslash }^2{\text{MeV}}^{-1}$) for yrast bands in Nd isotopes with neutron numbers $N=64$ to $N=80$. For details see text.

Figure 11

Kinetic moments of inertia ${\mathcal{J}}^{\left(1\right)}\left({\hslash }^2{\text{MeV}}^{-1}\right)$ of ground state bands for the ${}^{130–140}\mathrm{Nd}$ isotopes, as functions of rotational frequency $\omega$ (MeV). The red and blue symbols connected by continuous lines are for experimental [48, 49, 50, 51, 52, 53] and calculated values, respectively. For convenience experimental data for ${}^{136,138}\mathrm{Nd}$ are not shown at frequency $\omega >0.5$ MeV.

Figure 12

Ratio of $4^{+}$ and $2^{+}$ excitation energies (MeV) of Nd gs-band levels as a function of neutron number. Red and blue symbols are for experimental and calculated values, respectively. The dashed and dotted lines are for rotational and vibrational $R_{42}$ limits, respectively.

Figure 13

$B\left(E2\right)$ strengths. Red and black symbols are for experimental and calculated values (W.u.), respectively. Panels (a)–(d) are for gs-band transitions. Panels (e) and (f) are for $\gamma \to$ gs transitions. For details see text.

Figure 14

Excitation energies (MeV) of $\gamma$-band levels up to spin $I=8\hslash$. The red and black circles are for experimental and calculated values, respectively. The blue symbols are for $0_{\beta }^{+}$ and $2_{\beta }^{+}$ members of $\beta$-vibrational bands.

Figure 15

Experimental and calculated even-odd staggering parameter $S\left(I\right)$ values are shown as red and black symbols, respectively. The blue symbols are for asymmetric rotor model predictions.

Figure 16

$B\left(E2\right)$ ratio for $\gamma$- to gs-band transitions. Experimental and calculated values are shown as red and blue symbols, respectively.

Figure 17

Spectroscopic quadrupole moments $\left(e\mathrm{b}\right)$. Red symbol is for the ${}^{140}\mathrm{Nd}$ experimental $Q\left(2_1^{+}\right)$ value. Black and blue symbols are for calculated $Q\left(2_1^{+}\right)$ and $Q\left(2_{\gamma }^{+}\right)$ values, respectively.

Figure 18

Panels (a) and (b) are for charge radii and isotope shifts, respectively. Red and black symbols are for experimental and calculated values, respectively.

Figure 19

$E0$ transitions. Calculated ${\rho }^2\left(E0\right)$ rates (blue symbols) versus neutron numbers, from $N=70$ to $N=90$. The red symbol is the experimental value measured for ${}^{142}\mathrm{Nd}$. Open squares are for ${\rho }^2\left(E0\right)$ values determined from calculated isomer shifts.