Fragment Mass Distribution of Radioactive 238U* Nucleus

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Fragment Mass Distribution of Radioactive 238U* Nucleus

Gurvinder Kaur, Amandeep Kaur and Manoj K. Sharma*

School of Physics and Materials Science, Thapar University Patiala, Punjab E-mail:


The decay of compound nucleus 238U*, formed in the neutron induced reaction is studied using the dynamical cluster decay model (DCM) at two excitation energies lying across the Coulomb barrier. The role of deformations in the decay of 238U * has been studied by considering the quadrupole deformations (2) within the optimum orientation approach (i opt ) and with the spherical choice of fragmentation. The calculated results show an excellent agreement with the experimental data for the fission cross sections (fission).

1. Introduction

In recent times the study of radioactive nuclei has gained much more importance owing to their tremendous advantage in the field of science. To utilize the qualitative features of the radioactive nuclei requires a thorough understanding of the formation and dynamic aspects of these nuclei. In order to achieve this several major and minor actinides have been studied in various forms, neutron induced reactions being one of them.

The excitation functions of compound nucleus 238U* formed in n-induced reaction have been investigated by Burke et. al., [1] at a number of energies spread across the Coulomb barrier. In reference to this experiment [1], we intend to study the decay of 238U*compound nucleus using the dynamical cluster decay model

within optimum orientation (i opt) approach. The deformations i, in DCM are taken from the theoretical estimates of Moller and Nix [5] while the optimum orientations of the hot fusion process are employed in reference to [4].

The organization of paper is as follows: A brief account of the dynamical cluster-decay model (DCM) is presented in section 2. The calculations and results for fission excitation functions are discussed in section

3. Finally, the results are summarized in section 4.

  1. The Dynamical Cluster-Decay Model (DCM) The work presented here deals with the study of dynamics involved in the neutron induced reaction using Dynamical Cluster-decay Model (DCM) [2-4], where the decay of hot (T0) and rotating (0) compound nucleus with effects of deformations and orientations of two nuclei or fragments included is studied by applying dynamical collective clusterization process. The temperature T is related to CN excitation

    energy as

    ECN*=(ACN/9)T2-T (1)

    The DCM explains the nuclear dynamics by mass asymmetry coordinates defined as A=(A1-A2)/(A1+A2), the relative separation R, the multipole deformations i (=2, 3, 4), and orientations i (i=1,2) of two nuclei or fragments (1 and 2 represent respectively, the heavy and light fragments). With all these coordinates the compound nucleus decay cross-section for -partial waves is given by

    (DCM) [2-4]. In the present work, to have better

    l l max

    1)P P ; k



    understanding of the dynamics of 238U* system, the calculations have been done at extreme excitation

    k 2 l 0

    (2l 0


    energies lying across the Coulomb barrier i.e. at Ec.m.=0.67 MeV and at Ec.m.=18.60 MeV. The structural features in the decay of compound nucleus under study are examined in the form of potential energy surfaces. An interesting feature of DCM is that the deformation and orientation effects are duly incorporated in it. Thus

    in order to analyze the role of deformations, the fission

    where the maximum angular momentum max is fixed for the vanishing light particle cross-section LP 0. The preformation probability P0 refers to motion and the penetrability P to R motion. The penetration probability P in equation (2) is calculated using the WKB integral as.

    cross sections have been calculated using the dynamical

    2 Rb



    P exp {2[V R Qeff ]}2 dR


    cluster-decay model (DCM) for the spherical choice of fragmentation and with the inclusion of 2 deformations


    Ra, i.e. the first turning point of the penetration path(s) is defined as Ra=R1(1,T)+R2(1,T)+ R(T) = Rt(, T)

    + R(T). The R(T) is the neck-length parameter that

    inclusion of deformations higher R values are


    assimilates the neck formation effects between two nuclei. The preformation probability P0 is calculated by solving stationary Schrodinger equation in , at a fixed R = Ra, The expression for P0 is given as



    Preformation probability P








    Ec.m.=0.67 MeV T=0.53 MeV

    Sph. max=107

    2 def. max=103 (a)

    238 *


    Ec.m.=18.60 MeV T=0.99 MeV

    Sph. max=134

    2 def. max=133 (b)

    1n + 237U 238U* A + A

    P Ai 2



    n + U U A1 + A2 1 2

    0 R ACN


    Ec.m.=0.67 MeV T=0.53 MeV


    =18.60 MeV


    where are the smooth hydrodynamical masses [6].

  2. Results and Discussions









    1n + 237U 238U* A + A

    0 28 56 84 112 140 168 196 224 0 28 56 84 112 140 168 196 224

    Fragmentation potential V (MeV)




    1 2

    17B 55K

    Ec.m.=0.67 MeV


    Ec.m.=18.60 MeV T=0.99 MeV

    Sph. max=134

    2 def. max=133

    Fragment mass (Ai)

    Figure2. Same as fig.1 but for preformation probability

    T=0.53 MeV =max

    75 Sph.




    involved being 1.1fm and 1.250fm at extreme energies.








    2 def. max=103


    Ec.m.=0.67 MeV T=0.53 MeV



    Ec.m.=18.60 MeV T=0.99MeV

    Sph. R=1.110 fm

    2 def. R=1.250 fm


    Fig.2 shows the variation of P0 as function of fragment mass Ai. Comparing Fig. 2(a,b) and 2(c,d) it is observed that at lower angular momentum values the contribution of evaporation residues is more whereas at

    higher angular momentum the fission fragments are

    30 Sph. R=0.788 fm

    15 2 def. R=1.100 fm



    dominating. Although the structure is almost similar for

    0 1n + 237U 238U* A + A


    1n + 237U 238U* A + A (d)

    spherical and deformed choices, the role of deformation

    1 2 1 2

    0 16 32 48 64 80 96 112 0 16 32 48 64 80 96 112

    Fragment mass (A2)

    Figure1. Fragmentation potential for spherical and 2 deformed approach at extreme energies across the barrier at (a,b) = max and (c,d) = 0 .

    The structural effects in the dynamics of n+237U238U* reaction are addressed on the basis of the fragmentation potential V (MeV) and the preformation probability of the decaying fragments. Fig.1 shows the variation of fragmentation potential as a function of fragment mass (A2) at both the energies across the barrier for = max

    [parts (a,b)] and =0 [parts (c,d)]. Comparing the

    potential energy surfaces for spherical and deformed choice of fragments it is observed that fragmentation potential remains identical for evaporation residue (A24) and fission fragments. A slight change in structure in the intermediate mass region is observed on going from below barrier to above barrier energy. The only parameter of the model, R used to obtain the fission cross setions of 0.42b and 1.2b is different for spherical and 2 choice of fragmentation being 0.788fm and 1.110fm for spherical case at below barrier energy

    i.e. Ec.m.=0.67MeV and at above barrier energy, Ec.m.=18.60MeV respectively. However, with the

    is more evident at lower energy. The fragment mass distribution is more symmetric for spherical fragmentation and is relatively lesser for the 2 choice of fragmentation.

  3. Conclusion

    The DCM based fission cross sections for the decay of 238U* are in nice agreement with experimental data. The effect of deformations is more significant at below barrier region as compared to that for above barrier. Moreover, the structure of potential energy surfaces is almost identical for evaporation residues and fission fragments for both the spherical and deformed choice of fragmentation. The mass distribution is more symmetric for the spherical case and relatively less for 2 deformed choice.

  4. References

[1] J. T. Burke, Phys. Rev. C 73, 054604, 2006.

  1. R. K. Gupta, Clusters in Nuclei, Lecture Notes in Physics

    818, Vol. I, p.223, ed. C. Beck, Berlin, Heidelberg, 2010

  2. G. Kaur and M. K. Sharma, Phys. Rev. C 87, 044601, 2013;G. Sawhney, G. Kaur, M. K. Sharma, and R. K. Gupta Phys. Rev. C 88, 034603, 2013.

  3. R. K. Gupta, et al, J. Phys. G 31, 631, 2005

  4. P. M¨oller, J. R. Nix, W. D. Myers, W. J. Swiatecki, At. Nucl. Data Tables 59, 185, 1995.

  5. H. Kr¨oger and W. Scheid, J. Phys. G: Nucl. Part. Phys 6, L85, 1980.

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