Nucleon transfer in heavy ion reactions
An analytical formula is derived for the amplitude for transfer of a nucleon in quasi-elastic reactions between heavy ions. The derivation takes advantage of the semiclassical conditions found in peripheral collisions between heavy ions. The relative motion of the two nuclei is treated classically a...
| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
1985
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| _version_ | 1797111305598926848 |
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| author | Lo Monaco, L |
| author2 | Brink, DM |
| author_facet | Brink, DM Lo Monaco, L |
| author_sort | Lo Monaco, L |
| collection | OXFORD |
| description | An analytical formula is derived for the amplitude for transfer of a nucleon in quasi-elastic
reactions between heavy ions. The derivation takes advantage of the semiclassical conditions
found in peripheral collisions between heavy ions. The relative motion of the two nuclei
is treated classically and the transfer amplitude is calculated by a perturbation method.
Under the approximation of small overlap between the nuclear potentials, the semiclassical
amplitude is reduced to a surface integral. This can be calculated analytically by using
Hankel function forms for the bound-state wavefunctions and by approximating the actual
orbit by a constant velocity orbit tangential to it at the distance of closest approach.
These approximations seem reasonable in strong absorption conditions. Corrections to the
formula of the amplitude are evaluated. The analytical form of the amplitude exhibits an
exponential behaviour as a function of the distance of closest approach. The decay constant
of the exponential is given explicitly and it is found to be an important parameter
of the reaction. Kinematical conditions for maximum transfer are derived which relate the
incident energy to the reaction Q-value. The physical interpretation of the amplitude is
discussed. In the case of proton transfer, the effect of Coulomb potential results in a shift
of the binding energy of the proton. With this prescription we still obtain the same form
of the transfer amplitude for both neutrons and protons. The formula for the semiclassical
tranfer amplitude is used to calculate angular distributions within a simplified formalism
derived from the distorted wave Born approximation (DWBA). The reactions considered
are <sup>208</sup> pb(<sup>16</sup>O,<sup>15</sup>O)<sup>209</sup>pb , <sup>26</sup>mg(<sup>11</sup>B,<sup>10</sup>B)<sup>27</sup>mg and <sup>34</sup>S(<sup>32</sup>S, <sup>33</sup>S) <sup>33</sup>S for neutron transfer
and <sup>208</sup>pb(<sup>16</sup>O,<sup>15</sup>N)<sup>209</sup> Bi for proton transfer. It is found that the shapes of the present
angular distributions agree with full DWBA calculations but the magnitude of the former
depends on whether the distance of closest approach is that of the initial channel, the final
channel or some average of the two. Conditions for the selective population of definite
states are discussed in relation to the reaction Q-value, energy and initial and final states
involved. It is found that an inversion of the selectivity with respect to the spins of the
initial and final state occurs when the energy of relative motion at distance of closest apprach
equals the reaction Q-value. An approximate formula for the angle-integrated cross
section has also been derived. |
| first_indexed | 2024-03-07T08:06:56Z |
| format | Thesis |
| id | oxford-uuid:a79d2f08-7cfc-4d40-a58a-30cffd96d899 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:06:56Z |
| publishDate | 1985 |
| record_format | dspace |
| spelling | oxford-uuid:a79d2f08-7cfc-4d40-a58a-30cffd96d8992023-11-06T12:18:52ZNucleon transfer in heavy ion reactionsThesishttp://purl.org/coar/resource_type/c_db06uuid:a79d2f08-7cfc-4d40-a58a-30cffd96d899EnglishHyrax Deposit1985Lo Monaco, LBrink, DMAn analytical formula is derived for the amplitude for transfer of a nucleon in quasi-elastic reactions between heavy ions. The derivation takes advantage of the semiclassical conditions found in peripheral collisions between heavy ions. The relative motion of the two nuclei is treated classically and the transfer amplitude is calculated by a perturbation method. Under the approximation of small overlap between the nuclear potentials, the semiclassical amplitude is reduced to a surface integral. This can be calculated analytically by using Hankel function forms for the bound-state wavefunctions and by approximating the actual orbit by a constant velocity orbit tangential to it at the distance of closest approach. These approximations seem reasonable in strong absorption conditions. Corrections to the formula of the amplitude are evaluated. The analytical form of the amplitude exhibits an exponential behaviour as a function of the distance of closest approach. The decay constant of the exponential is given explicitly and it is found to be an important parameter of the reaction. Kinematical conditions for maximum transfer are derived which relate the incident energy to the reaction Q-value. The physical interpretation of the amplitude is discussed. In the case of proton transfer, the effect of Coulomb potential results in a shift of the binding energy of the proton. With this prescription we still obtain the same form of the transfer amplitude for both neutrons and protons. The formula for the semiclassical tranfer amplitude is used to calculate angular distributions within a simplified formalism derived from the distorted wave Born approximation (DWBA). The reactions considered are <sup>208</sup> pb(<sup>16</sup>O,<sup>15</sup>O)<sup>209</sup>pb , <sup>26</sup>mg(<sup>11</sup>B,<sup>10</sup>B)<sup>27</sup>mg and <sup>34</sup>S(<sup>32</sup>S, <sup>33</sup>S) <sup>33</sup>S for neutron transfer and <sup>208</sup>pb(<sup>16</sup>O,<sup>15</sup>N)<sup>209</sup> Bi for proton transfer. It is found that the shapes of the present angular distributions agree with full DWBA calculations but the magnitude of the former depends on whether the distance of closest approach is that of the initial channel, the final channel or some average of the two. Conditions for the selective population of definite states are discussed in relation to the reaction Q-value, energy and initial and final states involved. It is found that an inversion of the selectivity with respect to the spins of the initial and final state occurs when the energy of relative motion at distance of closest apprach equals the reaction Q-value. An approximate formula for the angle-integrated cross section has also been derived. |
| spellingShingle | Lo Monaco, L Nucleon transfer in heavy ion reactions |
| title | Nucleon transfer in heavy ion reactions |
| title_full | Nucleon transfer in heavy ion reactions |
| title_fullStr | Nucleon transfer in heavy ion reactions |
| title_full_unstemmed | Nucleon transfer in heavy ion reactions |
| title_short | Nucleon transfer in heavy ion reactions |
| title_sort | nucleon transfer in heavy ion reactions |
| work_keys_str_mv | AT lomonacol nucleontransferinheavyionreactions |