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Discuss the energy spectrum of the compound nucleus. What is radiation
width of the level? Express it in energy unit. Explain in detail the conditions
which characterize the discrete, quasidiscrete and continuum spectrum.
The compound nucleus is a complex quantal system with many digress of freedom in highly excited states in which the excitation energy is not lower than the absorbed particle separation energy. Let us consider a compound nucleus ‘C’ produced by the capture of a particle ‘a’ by a nucleus ‘A’ : a + A →C^ (1) Let the target nucleus be described by the mass number ‘A’ and charge number ‘Z’, and let the probe be a neutron ‘n’. Then the system ‘C’ is a nucleus with the mass number A+ 1 and the charge number ‘Z’. Fig. 1 gives a sketch of the nuclear energy spectrum. The energy reference point is taken to the ground state energy, Ec = mcC 2 , then the energy E of the nucleus C in the state is equal to the excitation energy. Fig.1 The energy spectrum of the nucleus. Lecture - 05
The nuclear ground state energy is equal to zero, E 0 = 0. The excited states are associated with positive discrete energies, E 1 , E 2 , E 3 … .., etc. In contrast to the ground state, the excited states have finite lifetimes by virtue of probable radiation transitions into the lower states. The reciprocal of the level lifetime () is determined by the - quantum emission probability per unit time. When expressed in units, this quantity is referred to as the radiation width of the level. λ (^) ( )
^ (2)
Within the context of the uncertainty relation Et = ℏ, the quantity may be treated as the energy uncertainty E = for a state existing for a finite time, t = ()^. The level density increases with growing excitation energy. Excitation energy sufficient for some particle to be separated from the system C (the lowest threshold Smin of the system disintegration into two subsystems) determines the continuum spectrum boundary. Energy Ec of a compound nucleus produced by the process of Eq ( 1 ) lies in the continuum spectral range C
E C = E A + E a + S aA
For the quasidiscrete spectrum to occur for energies higher than Smin, the excited state lifetime must be sufficiently long, i.e., the width must be smaller than the distance D between the neighbor levels: λ λ
D^ (4)
Quasidiscrete levels get gradually wider with growing energy, as the number of probable disintegration ways increases. The total level width may be presented as the sum λ λ λ a γ a
where a is the partial width associated with the emission of a particle a, is the radiation width; summation extends over all the open channels. The total level width increases with growing energy by virtue of three factors: 1 ) More particles can be emitted from a higher level; 2 ) Various final states of the residual nucleus can occur for high excitation energies; 3 ) Individual particle widths a increase with growing energy too. It is evident that one may regard the spectrum as quasidiscrete only provided condition of Eq ( 4 ) is satisfied, i.e., for widths smaller than the interlevel distances.
With increasing excitation energy, the interlevel distances become so small, and the widths grow so large, that levels overlap and thus the spectrum becomes quasicontinuum. Peculiarities of the discrete spectrum may be observed, however, even in this range by virtue of level density fluctuations and specific selection rules. The level character undergoes qualitative modifications only for excitation energies close to the total binding energy (about 6 - 8 MeV per particle). For this range, one particle can concentrate sufficient separation energy as a rule rather than as an exception. Under such conditions, the level spectrum becomes really continuum.
