Determination of fission barrier height using the multinucleon transfer reactions

K.R. Kean1,2), K. Nishio2), K. Hirose2), M.J. Vermeulen2),
H. Makii2), R. Orlandi2), K. Tsukada2), A.N. Andreyev2,3),
I. Tsekhanovich4), and S. Chiba1)
1): Tokyo Tech, 2): Heavy Element Nuclear Science Gr,3): Univ. York. 4): Univ. Bordeaux

The fission barrier height, introduced by Bohr and Wheeler, is
one of the most fundamental quantities to describe fission. In theclassical liquid-drop picture, the fission barrier is created by abalance between the attractive surface tension and the repulsive
Coulomb force of the nascent fission fragments, which evolves
as a function of deformation in a rather simple (parabolic) way.
The fission barrier of the macroscopic liquid-drop approach isdramatically modified by introducing shell correction energy,
which results in a double-humped shape, as well known for
typical actinide nuclei. Experimental data of the fission barrierheight can be a benchmark for fission theory, thus the data areessential to develop a fission model with a high predictive power.
Up to now, fission barrier profile in actinide nuclei has been
derived using neutron-induced fission and nucleon-transfer
reactions with light projectiles, such as (𝑑𝑑, 𝑝𝑝) , (𝑡𝑡, 𝑝𝑝) , and( 3He, 𝑑𝑑) reactions [1]. In these methods, the fission probability
is usually measured as a function of excitation energy 𝐸𝐸 ∗ of thecompound nucleus that can fission. The height of the fission
barrier is nearly equal to 𝐸𝐸 ∗ of the nucleus at which the fission
probability 𝑃𝑃f (𝐸𝐸 ∗ ) increases rapidly. However, such methods
require the use of stable or long-lived target nuclei, which limits
the range of accessible nuclei to be studied. This is why there
exist only 33 nuclei in the best-suited actinide region, of which
the fission barrier data are available.
Recently, we have demonstrated that reliable fission data, e.g.,
fission fragment mass distribution (FFMD), can be obtained via
multinucleon transfer (MNT) reactions of an 18O beam on
actinide targets, such as 232Th, 238U, etc. [2,3]. Due to a large
number of MNT channels accessible in reactions with an 18O
induced reactions, low-energy fission data of about 12 nuclides
can be simultaneously taken in a single experiment. In the studyof the 18O + 238U reaction, for instance, the FFMDs for 12
isotopes of uranium, neptunium, and plutonium are reported. The
results indicate the potential use of the MNT approach to expand
the fission barrier data. Here, we report the results of the MNTreaction of 18O + 237Np to derive fission barrier data [4].
The MNT reaction of 18O + 237Np was studied to obtain fission
barrier data, using the 162 MeV 18O -beam supplied from theJAEA tandem accelerator facility in Tokai. A segmented silicon
𝛥𝛥𝛥𝛥-𝐸𝐸 telescope was mounted at the forward angle to detect theejectile nucleus generated in the MNT reaction. Taking advantageof the high resolving power to identify produced isotopes, we
could unambiguously identify the ejectile nucleus, and thus thecorresponding compound nucleus as well as the total excitationenergy of the system 𝐸𝐸 ∗ after the reaction. Here, we assume that
all the excitation energy is stored in the compound nucleus, i.e.
nucleus whose fission barrier height is to be derived. The kineticenergy spectrum of the ejectile nucleus can be directlytransformed to the excitation-energy 𝐸𝐸 ∗ distribution of thecompound nucleus 𝑃𝑃ex (𝐸𝐸 ∗ ). Fission of the compound nucleus isidentified using multiwire proportional counters. The
coincidence spectrum between ejectile nucleus and fission
fragments is divided by 𝑃𝑃ex (𝐸𝐸 ∗ ) to obtain the excitation functionof fission probability 𝑃𝑃f (𝐸𝐸 ∗ ) , corrected by the detection
efficiency of fission fragments.
Fig.1 shows the fission probability of 240Pu obtained in the237
Np( 18O, 15N) 240Pu reaction. At the excitation energy 𝐸𝐸 ∗ ofaround 6 MeV, the fission probability sharply rises, indicating thelocation of the fission barrier. Fission barrier is derived by fitting
the data points with the Hill-Wheeler’s expression for barrier
penetration which includes the barrier height 𝐵𝐵f , see the solid
curve in Fig.1. In this method, we obtained 𝐵𝐵f = 6.25(32) MeV
for 240Pu . As our measurement is sensitive to the fission
threshold, which corresponds to the higher fission-barrier valueof the double-humped barrier shape, we compared our value tothe higher one, inner barrier for the case of 240Pu. The data agree
well with 5.80(20) MeV from the 238Pu(𝑡𝑡, 𝑝𝑝) 240Pu reaction [5]240Pu

Excitation Energy, E * (MeV)

Fig.1 Fission probability of 240Pu with excitation energy E*. Blue
points indicate experimental data, while the green curve is a theoreticalfit. The excitation energy where the fission probability increases(around 6 MeV) corresponds to the fission barrier height.

and 6.05 MeV from RIPL3 data [6].We also determined thefission barriers of 239Pu and 239Np , populated in the237
Np( 18O, 16N) 239Pu and 237Np( 18O, 16O) 239Np reactions,respectively. The value 𝐵𝐵f ( 239Pu) = 6.14(12) MeV and𝐵𝐵f ( 239Np) = 5.86(09) MeV also agree with literature data
within error. Our results showed the validity of deriving thefission barrier height in the MNT reactions using18O beam. Othertransfer channels can be also applicable to obtain the fission
barrier data. Use of more exotic target materials such as 244Pu,243
Am, 248Cm , 249Bk , 249Cf , and 254Es would further expand
the information on the fission barriers of heavier and neutron-richisotopes.
References[1] In the following, the expression “𝑋𝑋 (𝑎𝑎 , 𝑏𝑏)𝑌𝑌” represents a nuclear
reaction (nucleon transfer or nucleon exchange) “ 𝑎𝑎 (projectile) +𝑋𝑋 (target) → 𝑏𝑏 (ejectile) + 𝑌𝑌 (compound nucleus) ”, meanwhile“(𝑎𝑎 , 𝑏𝑏)" indicates the same with anonymous 𝑋𝑋 and 𝑌𝑌.
[2] R. Léguillon et al., Phys. Lett. B 761, 125 (2016).
[3] K. Hirose et al., Phys. Rev. Lett. 119, 222501 (2017).
[4] K.R. Kean et al., Phys. Rev. C 100, 014611 (2019).
[5] B.B. Back et al., Phys. Rev. C 9, 1924 (1974).
[6] https://www-nds.iaea.org/RIPL-3/fission/empirical-barriers.dat