Second-order equation of state with the Skyrme interaction: Cutoff and dimensional regularization with the inclusion of rearrangement terms

We evaluate the second-order (beyond-mean-field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the zero-range character of this interaction. An adjustment of the force parameters is then performed in both cases to remove any double counting generated by the explicit computation of beyond-mean-field corrections with the Skyrme force. In addition, we include at second order the rearrangement terms associated with the density-dependent part of the Skyrme force and discuss their effect. Sets of parameters are proposed to define new effective forces which are specially designed for second-order calculations in nuclear matter.

Figure 1

(a) Second-order EOS of symmetric matter computed for several values of the cutoff $\mathrm{\Lambda }$ and compared with the mean-field EOS; (b) second-order correction to the energy per particle for symmetric matter. The used parameters are those of SLy5.

Figure 2

(a) Second-order pressure; (b) second-order incompressibility modulus. The used parameters are those of SLy5.

Figure 3

Difference between the refitted second-order EOS and the mean-field EOS for symmetric matter.

Figure 4

Second-order refitted EOS compared with the SLy5-mean-field EOS for symmetric matter.

Figure 5

(a) Difference between the second-order pressure and the mean-field-SLy5 value; (b) same as in panel (a), but for the incompressibility modulus. The black arrow indicates the maximum deviation of the compressibility from the mean-field-SLy5 value at the saturation point.

Figure 6

(a) Second-order pressure compared to the SLy5-mean-field curve; (b) same as in panel (a), but for the incompressibility modulus.

Figure 7

(a) Second-order EOS of neutron matter for several values of the cutoff, calculated with the SLy5 parameters, and SLy5-mean-field EOS; (b) second-order correction.

Figure 8

Difference between the refitted EOS and the SLy5-mean-field EOS for neutron matter.

Figure 9

Refitted second-order EOS for neutron matter compared with the SLy5-mean-field EOS.

Figure 10

(a) Second-order EOS of asymmetric matter ($\delta =$ 0.5) for several values of the cutoff, calculated with the SLy5 parameters, and SLy5-mean-field EOS; (b) second-order correction.

Figure 11

Difference between the refitted EOS and the SLy5-mean-field EOS for asymmetric matter ($\delta =$ 0.5).

Figure 12

Refitted second-order EOS for asymmetric matter ($\delta =$ 0.5) compared with the SLy5-mean-field EOS.

Figure 13

Second-order EOS's obtained with the simultaneous fit of symmetric matter (a), asymmetric matter with $\delta =0.5$ (b), and neutron matter (c) compared with the SLy5-mean-field corresponding curves.

Figure 14

Difference between the global refitted EOS's and the SLy5-mean-field EOS's for symmetric (a), $\delta =0.5$ (b), and neutron (c) matter.

Figure 15

Pressure (a) and incompressibility modulus (b) computed with the parameters of the simultaneous fit and compared with the mean-field curves.

Figure 16

Differences with respect to the mean-field curves of the pressure (a) and incompressibility modulus (b), computed with the parameters of the simultaneous fit.

Figure 17

(a) Dimensional-regularized second-order EOS for symmetric matter compared with the corresponding SLy5-mean-field EOS. (b) Second-order correction.

Figure 18

Refitted dimensional-regularized second-order EOS for symmetric matter compared with the corresponding SLy5-mean-field EOS.

Figure 19

(a) Dimensional regularized second-order EOS for neutron matter compared with the corresponding SLy5-mean-field EOS. (b) Second-order correction.

Figure 20

Best fit for dimensional regularized second-order EOS of neutron matter compared with the SLy5-mean-field EOS.

Figure 21

(a) Dimensional-regularized second-order EOS for asymmetric matter in the case $\delta =0.5$ compared with the corresponding SLy5-mean-field EOS. (b) Second-order correction.

Figure 22

Best fit for dimensional-regularized second-order EOS for asymmetric matter ($\delta =$ 0.5) matter compared with the SLy5-mean-field EOS.

Figure 23

Same as Fig. 1 but with an effective mass computed within the mean-field approximation.

Figure 24

Same as Fig. 7 but with an effective mass computed within the mean-field approximation.

Figure 25

Second-order EOS's for symmetric (a) and pure neutron matter (b) adjusted on the SLy5-mean-field EOS's, with an effective mass equal to the mean-field effective mass, for different values of the cutoff.

Figure 26

Second-order EOS's for symmetric (a) and pure neutron matter (b) compared with the SLy5-mean-field EOS's, calculated with the SLy5 parameters for the case where $m^{*}=m$ and rearrangement terms are neglected (red circles and dotted line), for the case where a mean-field effective mass is used and rearrangement terms are neglected (gree squares and dotted line), and for the case where a mean-field effective mass is used and rearrangement terms are included (blue dashed line).

Figure 27

Second-order EOS's for symmetric (a) and pure neutron matter (b) adjusted on the SLy5-mean-field EOS's, with an effective mass equal to the mean-field effective mass and with the inclusion of the rearrangement terms, for different values of the cutoff.

Figure 28

Same as in Fig. 18, but with an effective mass equal to the mean-field effective mass and with the inclusion of the rearrangement terms.

Figure 29

Same as in Fig. 28, but for neutron matter.