Abstract
We present a recently developed theory for the inclusive breakup of three-fragment projectiles within a four-body spectator model \cite{CarPLB2017}, for the treatment of the elastic and inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei in $A\,(a,b)\,X$ / $a = x_1 + x_2 + b$ collisions. The four-body theory is an extension of the three-body approaches developed in the 80's by Ichimura, Autern and Vincent (IAV) \cite{IAV1985}, Udagawa and Tamura (UT) \cite{UT1981} and Hussein and McVoy (HM) \cite{HM1985}. We expect that experimentalists shall be encouraged to search for more information about the $x_{1} + x_{2}$ system in the elastic breakup cross section and that also further developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the $b$ spectrum.
Highlights
We report a recently developed theory to treat the inclusive breakup of three-fragment weakly bound nuclei [1]
Quite recently this theory was applied to the (d,p) reaction [19,20,21, 23] as a mean to test the validity of the Surrogate Method [24,25,26], employed to extract neutron capture and fission cross sections of actinide target nuclei, such as 238U, 232Th, of importance for the development of generation fast breeder reactors
We have reported in this contribution that the general structure of the CFH cross section in the DWBA limit is similar in structure to the 3B one, with the full post form, which can be written as the sum of the prior four-body Udagawa and Tamura (UT) cross section plus the four-body Hussein and McVoy (HM) one plus an interference term when the 4B source term detailed in Eq (33) is used to compute the inelastic part of the inclusive cross-section
Summary
We report a recently developed theory to treat the inclusive breakup of three-fragment weakly bound nuclei [1]. Our theory is an extension of the inclusive breakup models used for incomplete fusion reactions and in the surrogate method with two fragment projectiles. The threebody approach was developed in the 80’s by Ichimura, Autern and Vincent (IAV) [2], Udagawa and Tamura (UT) [3] and Hussein and McVoy (HM) [4]. These three-body theories were extended to obtain the fragment yield in the reaction A (a, b) X, where the projectile is a = x1 + x2 + b. We expect that these developments could stimulate experimentalists to search for more information about the x1 + x2 system in the elastic breakup cross section, and that further theoretical developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the b spectrum
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