Evidence of dynamical dipole excitation in the fusion-evaporation of the ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$ heavy system

The excitation of the dynamical dipole mode along the fusion path was investigated for the first time in the formation of a heavy compound nucleus in the $A\sim 190$ mass region. The compound nucleus was formed at identical conditions of excitation energy and spin from two entrance channels: the charge-asymmetric ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$ and the nearly charge-symmetric ${}^{48}\mathrm{Ca}+{}^{144}\mathrm{Sm}$ at $E_{\text{lab}}=11$ and 10.1 MeV/nucleon, respectively. High-energy $\gamma$ rays and light charged particles were measured in coincidence with evaporation residues by means of the MEDEA multidetector array (Laboratori Nazionali del Sud, Italy) coupled to four parallel plate avalanche counters. The charged particle multiplicity spectra and angular distributions were used to pin down the average excitation energy, the average mass, and the average charge of the compound nucleus. The $\gamma$-ray multiplicity spectrum and angular distribution related to the nearly charge-symmetric channel were employed to obtain new data on the giant dipole resonance in the compound nucleus. The dynamical dipole mode excitation in the charge-asymmetric channel was evidenced, in a model-independent way, by comparing the $\gamma$-ray multiplicity spectra and angular distributions of the two entrance channels with each other. Calculations of the dynamical dipole mode in the ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$ channel, based on a collective bremsstrahlung analysis of the reaction dynamics, are presented. Possible interesting implications in the superheavy-element quest are discussed.

Figure 1

(a) Fast component vs total energy and (b) time of flight vs total energy bidimensional plots obtained for a ${\mathrm{BaF}}_2$ in the ring centered at ${\theta }_{\text{lab}}=51.5^{\circ }$ in the low-gain energy range for the reaction ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$; (c) time of flight vs total energy of the same detector is shown for events included in the contour of panel (a). The $\gamma$ rays retained in the analysis are obtained by applying both of the contours shown in panels (a) and (c).

Figure 2

(a) Energy loss $\mathrm{\Delta }E$ vs time of flight bidimensional plot obtained with one of the PPACs for the ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$ reaction. The numbers indicate different physical processes (see text). The evaporation residues are marked with the number 3. (b) Velocity distribution of the evaporation residues retained in the analysis. The arrows correspond to the average velocity of the distribution, $V_{CN}$, and the center-of-mass velocity $V_{\text{c.m.}}$, which is the complete fusion value of $V_{CN}$ for full linear momentum transfer. In the figure, the velocity is not corrected for the energy loss of the evaporation residues in the target.

Figure 3

(a), (c) Laboratory proton multiplicity spectra obtained at various angles in coincidence with the evaporation residues. For both reactions the angles are (from top to bottom) $51.5^{\circ },68.1^{\circ },111.9^{\circ },128.5^{\circ }$, and $159.7^{\circ }$. The solid lines show the result of the simultaneous fit with two sources described in the text. (b),(d) Laboratory proton multiplicity spectra at two angles. The solid lines are the result of the fit with two sources. The dashed and dotted lines represent the intermediate-velocity source and the slow source components, respectively.

Figure 4

As in Fig. 3 for $\alpha$ particles.

Figure 5

High-energy range of the center-of-mass $\gamma$-ray multiplicity spectra, obtained with detectors centered at polar angles from $51.5^{\circ }$ to $128.5^{\circ }$, in coincidence with the evaporation residues for the ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$ (solid squares) and the ${}^{48}\mathrm{Ca}+{}^{144}\mathrm{Sm}$ (open circles) reaction. The solid line represents the bremsstrahlung component determined from the simultaneous fit of the data, as described in the text.

Figure 6

(a) Center-of-mass bremsstrahlung-subtracted $\gamma$-ray multiplicity spectrum of the charge-symmetric reaction ${}^{48}\mathrm{Ca}+{}^{144}\mathrm{Sm}$, obtained with detectors centered at polar angles from $68.1^{\circ }$ to $128.5^{\circ }$, in coincidence with evaporation residues (symbols). The line represents the statistical $\gamma$-ray spectrum calculated with the code cascade and folded with the response function of the considered ${\mathrm{BaF}}_2$ rings. The cascade calculation was done by using the Puhlhofer prescription for the level density parameter and with $a=A/9.5 {\mathrm{MeV}}^{-1}$ in the “high-energy” region. (b) The linearized plot obtained by dividing the spectra shown in panel (a) by the cascade spectrum and multiplied by the $E1$ absorption cross section, ${\sigma }_{\text{abs}}\left(E_{\gamma }\right)$, used in the cascade calculation. The parameters of ${\sigma }_{\text{abs}}\left(E_{\gamma }\right)$ are presented in the first row of Table 6. Panels (c) and (d) are as (a) and (b), respectively, obtained by using $a=A/11 {\mathrm{MeV}}^{-1}$ in the “high-energy” region. The corresponding parameters of ${\sigma }_{\text{abs}}\left(E_{\gamma }\right)$ are presented in the second row of Table 6.

Figure 7

(From top to bottom) The same as in Fig. 6 with the parameters of ${\sigma }_{\text{abs}}\left(E_{\gamma }\right)$ presented in the third, fourth, and fifth rows of Table 6. Panels (a) and (b) correspond to the Reisdorf approach, (c) and (d) to the Charity approach, and (e) and (f) to the Ormand approach.

Figure 8

(a) Center-of-mass bremsstrahlung-subtracted $\gamma$-ray multiplicity spectra, obtained with detectors at polar angles from $51.5^{\circ }$ to $128.5^{\circ }$, in coincidence with evaporation residues. The solid (dashed) line represents the charge-asymmetric ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$ (nearly charge-symmetric ${}^{48}\mathrm{Ca}+{}^{144}\mathrm{Sm}$) reaction. (b) The symbols correspond to the difference between the experimental spectra of panel (a), i.e., the DD $\gamma$-ray spectrum. The solid line is a Lorentzian curve folded with the response function of the considered ${\mathrm{BaF}}_2$ rings with characteristics described in the text and presented in Table 7. (c) Percent difference between the data, i.e., ratio of the difference shown in panel (b) and the spectrum of the ${}^{48}\mathrm{Ca}+{}^{144}\mathrm{Sm}$ reaction shown in panel (a).

Figure 9

Energy dependence of the $a_2$ coefficient for (a) the ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$ and (b) the ${}^{48}\mathrm{Ca}+{}^{144}\mathrm{Sm}$ system. (c) $9\text{MeV}\le E_{\gamma }\le 15$ MeV $\gamma$-ray angular distribution of the ${}^{40}\mathrm{Ca}+{}^{152}\mathrm{Sm}$ (solid symbols) and ${}^{48}\mathrm{Ca}+{}^{144}\mathrm{Sm}$ (open symbols) reactions, corrected for the detection efficiency. The solid and dashed lines represent a fit of the data with a Legendre polynomial expansion ($a_2$ coefficients given in the text). (d) Angular distribution of the difference between the data of the two reactions appearing in panel (c), i.e., DD $\gamma$-ray angular distribution energy-integrated in the interval $9\text{MeV}\le E_{\gamma }\le 15$ MeV (symbols). The solid line is the result of a fit of the DD angular distribution with a Legendre polynomial expansion by using $a_2=-1$, the dashed line is a fit with $a_2=-0.84$ obtained within the BNV framework with the asystiff choice, and the dotted line shows the fit with an $a_2=-0.25$. All the quantities are in the center-of-mass reference frame.