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STABILITY OF EXCITED STATES AND BAND CUT-OFF IN LIGHT 4 N-NUCLEI
L. Satpathy, H. Friedrich, A. Weiguny
To cite this version:
L. Satpathy, H. Friedrich, A. Weiguny. STABILITY OF EXCITED STATES AND BAND CUT- OFF IN LIGHT 4 N-NUCLEI. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-269-C6-270.
�10.1051/jphyscol:1971662�. �jpa-00214880�
JOURNAL DE PHYSIQUE Colloque C6, supplbment au no 1 1 - 12, Tome 32, Novembre-Ddcembre 1971, page C6-269
STABILITY OF EXCITED STATES
AND BAND CUT-OFF IN LIGHT 4 N-NUCLEI
L. SATPATHY
Institut fur Kernphysik der KFA Jiilich, Germany and H. FRIEDRICH and A. WEIGUNY
Institut fiir Theoretische Physik der Universitat Miinster, Germany
RbumB. - En utilisant le modele des agregats a, la relative instabilitk, par dksintegration a, des etats excites du 12C et du 20Ne ainsi que la coupure des bandes de rotation qui en rksulte sont CtudiCes en calculant les knergies, aprks projection sur des Ctats de bon moment angulaire, en fonc- tion de la separation entre un agregat a et le noyau residuel.
Abstract. - Using the a-cluster model, the relative instability of excited states against a-decay and the resulting band cut-off in 12C and 2oNe are studied by calculating the angular momentum projected energies as functions of the separation between one a-particle and the residual nucleus.
From the low a-thresholds and the large a-widths we know that the instability of low excited states in light 4 N-nuclei is dominated by their probability of decaying into one a-particle plus residual nucleus.
To investigate this instability, and the resulting band cut-off, we use the wave functions of the a-cluster model of Brink [I], project out states of good angular momentum and study the dependence of the projected energies on the separation between one a-particle and the residual nucleus.
The a-cluster configurations are described by Slater determinants iP (R,, b) in which two protons and two neutrons occupy orbital states
qi O; exp { - (r - Ri)'/2 b2 ) ,
where r denotes the particle position. The cluster centers are given by the vectors R,, and their size is specified by b. Starting from the intrinsic states @, we apply the Peierls-Yoccoz method [I] to construct states Y' of good angular momentum I, and calculate the projected energies
EI = < Y I I HI Y f >/< !Pi I Y f >.
H = T - T,, + V ,,,, + V ,,,, is the complete
Hamiltonian of relative motion. As effective nuclear interaction we chose the B1 force of Brink and Boeker [2].
The procedure outlined above has been applied to some rotational states in "C and ''Ne which are discussed in the following.
In "C, the 7.65 MeV 0* state is of special interest because this state is supposed to be strongly deformed but no further members of a rotational band have been found yet. For this state, a triangular configu- ration with 0 = 1500 (see Fig. 1) has proven a good
approximation [3]. Keeping d = dl + d, constant, we minimized the energies E' for the positive parity states with respect t o d l . b was fixed a t 1.46 fm [3], For large d-values our model calculation favours configurations with constant dl -- 4 fm which corres- pond to a 'Be + a system. The dependence of the projected energies E' on d shows (Fig. 1) that the 6' state is unstable. The 4' state has negligible barrier, hence can also be considered unstable. In the limit d + co, all E' tend t o - 69 MeV so that the 0"
and 2' states are both metastable, although the barrier of the observed O+ state is very much wider.
Thus one may conclude that higher I-states either do not exist a t all or have such a short life time due to
@-decay that no rotational band is observable.
E (Me V )
150' z
FIG. 1. - a-cluster structure and rotationaI states in 12C.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971662
C6-270 L. SATPATHY AND H. FRIEDRICH AND A. WEIGUNY Ikeda et al. [4] have suggested that the ground state
band and the negative parity band at 5.8 MeV in 20Ne arise from one pear-shaped 160 + a intrinsic structure, which corresponds to our asymmetric bipyramid (Fig. 2). For various values of d = dl + d,
we have minimized the energy of the various states of the two K = 0 bands with respect to dl and d,.
The b-value was kept fixed a t 1.54 fm [3]. The resulting energy curves (Fig. 2) show no minimum for I = 12 and a negligible barrier for I = 10. The low states up to I = 4 are stable, whereas I = 6,8 are metastable as expected since these states are above a-threshold (4.7 MeV). The energies up to I = 6 compare well with experiment, the I = 8 state is too high. Our I = 1-, 3- - states are metastable in agreement with experiment ; the 5--state shows no minimum although this state is observed. The excitation energy of the band head (10.6 MeV) is too high. For large values of d we find dl
-
2.2 fm and dA e 1.6 fm for all cases while the energy tends to - 115 MeV. Such a configura- tion corresponds to a tetrahedral 160 plus one a-par- ticle. The equilibrium configurations of the I - , 3-- states show strong asymmetry (d2/d, cz 2.5) whereas the ground state band is based on much more symme- trical configurations (d2/dl-
1.6). This modifies the notion of Ikeda et al. [4].The energy curves E1(d) discussed in this paper may
FIG. 2. - "Ne configuration and rotational bands.
be related to the real part of the optical potential for a-nucleus scattering as long as the adiabatic approximation holds. The present calculation may then serve as a first step towards a microscopic treatment of the scattering of a-particles on light 4 N-nuclei in the framework of the generator coor- dinate method.
Acknowledgement. - One of us (L. S . ) wants to express his gratitude to Prof. A. Faessler for his hospi- tality a t the KFA Jiilich.
References
[I] BRINK (D. M.), Proc. Intern. School of Physics : FRIEDRICH (H.), SATPATHY (L.) and WEIGUNY (A.),
(( Enrico Fermi D, course 36 (Academic Press, Phys. Letters, 1971, 36B, 189.
1966).
[2] BR~NK (D. M.) and BOEKER (E.), Nuel. Phys., 1967, f41 IKEDA (K.), TAKIGAWA tN.) and Homucm
A 91, 1. Progr. Theor. Phys. Supplement, Extra Number,
131 FRIEDRICH (H.) and WEIGUNY (A.), Phys. Letters, 1968,464.
1971, 35B, 105.
