Statics and Dynamics of Compressed Nuclei

We especially study the surface tension of compressed nuclei and compression effects on the fission barrier. We analyse the consequences of this statical calculation on the dynamics of a vibrating nucleus using a h~drodynamical approach. In addition we present compression properties of excited homogeneous nuclear matter starting from a Fermi gas model. Nuclear experiments now are performed in an energy range where nuclei can be compressed and heated up to states which are far off from the well known region of saturation where pressure p and temperature T are vanishing. The structure of compressed eventually also heated nuclei is also of interest in astrophysics. The line of P-stability, nuclear decay properties, nuclear reactions,the single-particle level scheme etc. might be appreciably affected by an external pressure. In the present contribution we report on calculations of static compression properties of nuclei taking into account nuclear surface effects. These results are then used as input into a hydrodynamical model in order to study the dynamical behaviour of a nucleus in the O+-monopole state. In the last section we start from a Fermi gas model in order to derive compression properties of heated homoqeneous nuclear matter. I STATIC COMPRESSION PROPERTIES OF FINITE NUCLEI A value of K, 230 MeV for the incompressibility of infinite symmetric nuclear matter is now well established from calculations of static properties of finite nuclei as well as from analyses of the nuclear breathing mode /I/.In the case of finite nuclei this value is appreciably altered by surface effects /I/. The surface contribution to the incompressibility depends on the compression mode, i. e. on the way how the surface region is compressed. In order to study the surface incompressibility in the case of a plane surface we have carried out an analytical model calculation /2/ and also performed Hartree-Fock calculations usinq realistic Skyrme interactions / 3 / . For the simulation of the external pressure a densitydependent constraint Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984635 C6-290 JOURNAL DE PHYSIQUE has to be included which also depends on the compression ratio q = nc/n of the bulk density nc and the bulk saturation density no and on tRe surface compression mode characterized by a parameter B. In the case of the model energy density of ref. /2/ we obtain the following closed expression for the surface tension o, 1 ofq,P) = 3 oor4q 132 3q 1+3 + ql-Pj (21 oo is the surface tension at saturation. This expression reflects the essential features of the surface tension of compressed nuclear matter which are also found by constrained Hartree-Pock calculations /3/. The surface tension is found to be stationary at the saturation density no independently of the compression mode 8. Thus This theorem was first found by Myers and Swiatecki /4/ for the special case of a density multiplied by an overall factor, corresponding to our case I3 = 0. It is found that the surface tension for reasonable values of p is a maximum at the saturation density. Around no the surface tension turns out to be lowest for B = 1 which is the case where the density is antiscaled, i. e. where a compression in the bulk is combined with a more diffuse surface. The so-called scalinq of the density, B = 1/3, leads to a surface tension which is larger than for the case B = 1. We used this static result on the dependence of the surface tension on the bulk compression ratio q for a given surface compression mode p in order to calculate the dependence of the fission barriers of finite nuclei on compression. In a simple liquid drop description the fission barrier is determined by the interplay between Coulomb and surface effects. Since the surface tension is stationary at saturation the effect of compression on the fission barrier in first order comes only from Coulomb effects. Using the parameterization of Nix /5/ for the description of the nuclear deformation we obtain for the deformation energy Edef the following expression 7 '7 L L -. 3 3 22 Ed,f(~;qrB) = asurfA F(qrB)q {(BsUrf(~)-1)+Zm* ( B CO &) -1) 1