The shapes of even-even N =Z nuclei Ge, Se, Kr, Sr, and Zr are studied using deformed relativistic mean field theory. Large deformations (P=0.5) for ground states are found for Sr and ' Zr nuclei. The microscopic structures of these superdeformed configurations are emphasized.PACS number(s): 21.60. Jz, 21.10.Gv, 27.50.+e There has been much interest recently in the study of very neutron deficient N =Z nuclei near the proton-drip line [1 -5]. The experimental study of these exotic nuclei in the A =70 region has revealed several interesting features, such as the coexistence of different shapes and unusually large deformations (superdeformations, P=O. 5). It is thus an interesting problem to study theoretically the structures of these highly neutrondeficient nuclei. Many theoretical calculations are available. These include fully microscopic nonrelativistic Hartree-Fock models [6 -8], macroscopic-microscopic calculations with Yukawa [9,10], Woods-Saxon [10,11],and Nilsson potentials [12,13]. Also interacting-boson approximation (IBA) model studies have been performed in the A =70 mass region [13]. The analysis of the experimental results [2] shows that Sr is the most deformed nucleus in the region with P)0.4 and there is a drastic structural change between Z =N = 36 and Z =N = 38. Some of the calculations [9,13,14] indicate the same deformation for all N, Z =38,40 systems. Further some microscopic calculations [7] indicate that Sr would have a higher saddle between prolate and oblate shapes. In contrast with the above theoretical predictions the experimental observations [1 -3] indicate oblate shapes for the lighter isotopes and highly deformed prolate shapes for the heavier isotopes.Bearing in mind the nonuniqueness in the above theoretical descriptions, it is worthwhile to have a cornplete relativistic microscopic calculation to understand the shapes of these exotic nuclei. In this paper we study the properties of a number of such nuclei and the corresponding shape changes in the 3 =70 mass region by a relativistic mean field (RMF) calculation with interacting mesons and nucleons. Such a mean-field description of nuclei is known to give quite accurate binding energies and deformations for nuclei throughout the periodic table [15,16,20]. We start with the Lagrangian density [15,16,20] X=/, (i y"d~M)P;+ -, 'c)&oc)"cr -U(o ) g, Q; tP;o---, 'fI" 0,+-, 'm V" V"g ttr;y"Q V --'B-" Bq" + , 'm p" p"gP;y"r-g; p", 'F-"'F"--(1~3 ; )-ebb;y" Q =Q. +Q, = (3/4m)AR P,where R = 1.2A '~a nd Q is the quadrupole moment. This set gives a good account of various observables such as binding energies, rms radii, compressibility modulus, coefIicient of asymmetry energy [15,16,18,19], and other nuclear properties and hence we have used the nonlinear parameter set NL1 [20]. The major oscillator shells N, "=8 for nucleons and N, "=12 for bosons are used. For open shell nuclei pairing plays an important role. To take pairing into account, we have used the gap parameters given by Moeller et al. [10] in a constant gap approximation to pairing...
