Search for the fade out of a collective enhancement of the nuclear level density

The fade out of a collective enhancement of the nuclear level density is predicted (by an SU3 shell model) to give rise to a clear signature in the evolution of the spectral shape of evaporated charged particles with excitation energy. We have searched for this signature in the spectra of $\alpha$ particles emitted from ${}^{178}\mathrm{Hf}$ compound nuclei, with excitation energies between 54 and 124 MeV, formed in ${}^{18}\mathrm{O}+{}^{160}\mathrm{Gd}$ fusion reactions. The Gammasphere spectrometer provided us with the ability to construct channel-specific $\alpha$-particle spectra that could be compared to statistical-model calculations on a channel-by-channel basis. The expected clear signature of a rapid fade out of a collective enhancement was not found. The data are best reproduced by calculations that do not explicitly consider a collective enhancement and its fade out.

Figure 1

Quantities calculated for ${}^{168}\mathrm{Yb}$ with two different level density prescriptions. Curves labeled ${\rho }_{\mathrm{intr}}$ are for an intrinsic level density with $a=A/8$ MeV${}^{-1}$; curves labeled $\rho$ are with collective enhancement and fade out following the HJ prescription. (a) level densities, (b) statistical temperatures (dashed), and apparent temperatures from spectra of evaporated $\alpha$ particles $T_{\mathrm{app}}^{\alpha }$ (solid). The evolution of the $\alpha$-particle spectra, for $E^{*}$ of 50–200 MeV in steps of 25 MeV, are shown in (c) for $a=A/8$ MeV${}^{-1}$ and (d) when collective enhancement and fade out are included.

Figure 2

Statistical-model expectations for fusion-evaporation (solid) and fission (dotted) cross sections as a function of excitation energy.

Figure 3

Experimental configuration inside of the Gammasphere vacuum chamber.

Figure 4

$\Delta E$ (Si) vs time-of-flight (Si-RF) maps for $E_{\mathrm{beam}}=$ (a) 79.6 and (b) 117.3 MeV.

Figure 5

Ungated α-particle spectra. Scaling powers ($\times {10}^N$), are used for display purposes. Only statistical errors are shown. Lines show the results of a statistical-model calculation with $a=A/8$ MeV${}^{-1}$ and without the collective enhancement fade out.

Figure 6

γ-ray spectrum gated on α-particles for $E_{\mathrm{beam}}=156.1$ MeV. Lines associated with transitions in the $\alpha$6$n$ to $\alpha$10$n$ residues are indicated.

Figure 7

Total $H$ vs $K$ map for $E_{\mathrm{beam}}=156.1$ MeV. Regions G1–G5 represent gates designed to select spin regions.

Figure 8

$H$-$K$ gated α-particle spectra from gates G1–G5. Spectra labeled 1 through 10 [in (c)] correspond to the beam energies 78.7, 84.6, 90.9, 100.2, 108.5, 116.6, 126.2, 135.5, 145.6, and 156.1 MeV, respectively; see Table .

Figure 9

Apparent temperatures of (a) ungated and (b)–(f) $H$-$K$ gated $\alpha$-particle spectra. Dashed trendline for the $T_{\mathrm{app}}(E)$ for the ungated $\alpha$ spectra [from (a)] is reproduced, for reference, in each panel.

Figure 10

Channel-gated $\alpha$-particle spectra obtained from $\alpha \text{−}\gamma$ coincidences for (a) $\alpha 4n$, (b) $\alpha 6n$, and (c) $\alpha 8n$ channels. The fit [to Eq. (7)] spectra are shown as solid lines. The data and fit are labeled by the excitation energy in MeV on the right. Scaling powers ($\times {10}^N$) are used for display purposes.

Figure 11

$T_{\mathrm{app}}$ for the $\alpha 4n$, $\alpha 6n$, and $\alpha 8n$ channels are shown in all panels as symbols. (Circles and crosses for the $\alpha 4n$ channel result from employing the $6^{+}\to 4^{+}$ and $4^{+}\to 2^{+}$ transitions, respectively.) Data are compared with results of GEMINI simulations: (a) without collective enhancement fade out using $\tilde{a}=A/8$ MeV${}^{-1}$(solid line) and $A/10$ MeV${}^{-1}$ (dotted line); (b) without collective enhancement fade out using a variable level-density parameter ${\tilde{a}}_{\mathrm{var}}$; and (c) with HJ collective enhancement and fade out using $\tilde{a}=A/8$ MeV${}^{-1}$.

Figure 12

Same as Fig. 11, but showing total cross sections.

Figure 13

$H$ vs $K$ histograms gated on (a) 299 keV photons from ${}^{168}\mathrm{Yb}$ ($\alpha 6n$ channel) and (b) 228 keV photons from ${}^{166}\mathrm{Yb}$ ($\alpha 8n$ channel). The intensity scale is linear.

Figure 14

Total cross sections for the $4n$, $6n$, $8n$, and $10n$ channels are shown in all panels as symbols. (Points enclosed in circles are the result of an indirect normalization procedure, see text.) These data are compared with results of GEMINI simulations using (a) no collective enhancement fade out and $\tilde{a}=A/8$ MeV${}^{-1}$ (thick line) and $A/10$ MeV${}^{-1}$ (thin dotted line); (b) no collective enhancement fade out with ${\tilde{a}}_{\mathrm{var}}$; and (c) with HJ collective enhancement and fade out with $\tilde{a}=A/8$ MeV${}^{-1}$. Experimental data are repre- sented as diamonds for the $10n$, the 226 keV $(4^{+}\to 2^{+})$ tran- sition in ${}^{168}\mathrm{Hf}$; triangles for the $8n$, the 262 keV $(4^{+}\to 2^{+})$ transition in ${}^{170}\mathrm{Hf}$; circles for the $6n$, the 214 keV $(4^{+}\to 2^{+})$ transition in ${}^{172}\mathrm{Hf}$; and squares for the $4n$, the 311 keV $(6^{+}\to 4^{+})$ transition in ${}^{174}\mathrm{Hf}$.

Figure 15

Rotational enhancement coefficient $K_{\mathrm{rot}}$ for $A=178$ (solid) and $A=168$ (dashed). Ground-state deformation is $\beta =0.27$.

Figure 16

Apparent temperatures of total $\alpha$-particle spectra. Experimental data (circles) are reproduced in all panels. Lines are the results for the simulations: (a) without collective enhancement fade out and for $\tilde{a}=A/8$ and $A/10$ MeV${}^{-1}$; (b) without collective enhancement and with ${\tilde{a}}_{\mathrm{var}}=A/(7+1.3U/A)$ MeV${}^{-1}$; (c) with collective enhancement for $\tilde{a}=A/8$ MeV${}^{-1}$; and (d) with collective enhancement for ${\tilde{a}}_{\mathrm{Ign}}$.

Figure 17

Statistical temperatures (as a function of excitation energy) for $\tilde{a}=A/8$ MeV${}^{-1}$ with no collective enhancement and fade out (dashed), and including collective enhancement and fade out with a transition energy of 20 MeV and width of 5.5 MeV (thick solid line) and with a transition energy of 40 MeV and width of 10 MeV (thin solid line).

Figure 18

Experimental $\alpha 4n,\alpha 6n,$ and $\alpha 8n$ cross sections (symbols) are shown in both top and bottom panels. (Circles and crosses for the $\alpha 4n$ channel result from employing the $6^{+}\to 4$${}^{+}$ and $4^{+}\to 2$${}^{+}$ transitions, respectively.) Data are compared with statistical model calculations using $\tilde{a}=A/6$ MeV${}^{-1}$ (dashed), $\tilde{a}=A/8$ MeV${}^{-1}$ (solid), and ${\tilde{a}}_{\mathrm{Ign}}$ (dotted) in (a) with a transition energy of 40 MeV and width of 10 MeV and in (b) with a transition energy of 20 MeV and width of 5.5 MeV. Results for ${\tilde{a}}_{\mathrm{Ign}}$ are omitted in (b) because they predict roughly an order of magnitude too much $\alpha \mathit{xn}$ cross section.