C. M. Folden III Cyclotron Institute, Texas A&M University NN2012, San Antonio, Texas May 31, 2012

The heaviest elements are all produced artificially!

B f is the fission barrier. It is caused by a change in the surface and Coulomb energies at constant volume and density.  4  0

It was believed that nuclides with Z > 104 would have no macroscopic fission barrier. See J. Randrup et al., Phys. Rev. C 13(1), 229 (1976).

The reason we have so many transactinide elements is (partially) due to shell effects. Evidence: t ½ ( 257 Rf) = 4.7 s t ½ ( 270 Hs) = 3.6 s Cross sections etc. A. Sobiczewski and K. Pomorski, Prog. Part. Nucl. Phys. 58, 292 (2007).

We have used a number of “silver bullets” that have allowed us to create ever heavier elements: Z = (Cold Fusion Reactions): Shell Stabilization Near Z = 108, N = 162. Shell-Stabilized Targets (minor effect). Deformed Products (more on this later).

The shell effects for Z = (warm fusion reactions) are not as pronounced as for Z = (cold fusion reactions).

The evaporation residue cross section can be written as: Fission

Any change is the same as the opposite change in reverse: Estimate  n /  f by integrating over the level densities for neutron emission and fission: W. J. Świątecki, K. Siwek-Wilczyłńska, and J. Wilczyłński, Phys. Rev. C 71, (2005). R. Vandenbosch and J. R. Huizenga, Nuclear Fission (Academic Press, New York, 1973), pp

The level density is a function of energy:  (E) Expand around E = E* – B n and use d(ln  /dE  1/T:

The projectile has a major influence on  n /  f. Figure courtesy of D. A. Mayorov. Better Worse

We have used a number of “silver bullets” that have allowed us to create ever heavier elements: Z = (Cold Fusion Reactions): Shell Stabilization Near Z = 108, N = 162. Deformed Products (more on this later). Shell-Stabilized Targets (minor effect). Z = (Warm Fusion Reactions): The neutron-richness of 48 Ca is exceptional among available projectiles. It increases B f and decreases B n.

JINR studied the 244 Pu( 58 Fe, 4n) reaction and reported an upper limit cross section of 0.4 pb (0.74 pb at 84% confidence). GSI Experiments: 248 Cm( 54 Cr, 4n) Compare with 248 Cm( 48 Ca, 4n) 292 Lv:  EVR  3.3 pb 249 Cf( 50 Ti, 4n) Compare with 249 Cf( 48 Ca, 3n) :  EVR  0.5 pb 249 Bk( 50 Ti, 4n) (in progess) Other reactions have been proposed: 252 Cf( 50 Ti, 4n) U( 64 Ni, 4n)

162 Dy( 48 Ca, xn) 210-x Rn 248 Cm( 48 Ca, xn) 296-x Lv 162 Dy( 54 Cr, xn) 216-x Th 248 Cm( 54 Cr, xn) 302-x 120 ReactionProductN CN E cm – B Coul E*(CN)E*(CN) – Σ(B n,i ) 162 Dy( 48 Ca, 4n) 206 Rn MeV48 MeV15.6 MeV 162 Dy( 54 Cr, 4n) 212 Th MeV50 MeV15.8 MeV 248 Cm( 48 Ca, 4n) 292 Lv MeV41 MeV15.5 MeV 248 Cm( 54 Cr, 4n) MeV43 MeV15.9 MeV Column 4 shows the difference E cm – B, where E cm is the center of mass projectile energy and B is the average interaction (representing sum of Coulomb, centripetal, nuclear potentials) barrier height. E* CN is the excitation energy of the CN system. Column 6 gives the remaining excitation energy of a nucleus following emission of 4 neutrons each with binding energy S n. Values were calculated based on estimated projectile energy needed to remove 4 neutrons, leaving the residual nucleus with excitation energy below either the S n or B f, whichever is lower in energy.

As part of an upgrade sponsored principally by DOE, the K150 88” cyclotron is being recommissioned. Supplied by 6.4-GHz ECR Supplied by 14.5-GHz ECR

DeviceAcceptance  p/pB  max MARS9 msr±4%1.8 T m SHIP~4 msr±10%1.2 T m BGS45 msr±9%2.5 T m R.E. Tribble, R.H. Burch, and C.A. Gagliardi, NIMA 285, 441 (1989). R.E. Tribble, C.A. Gagliardi, and W. Liu, NIMB 56/57, 956 (1991).

Difference in dotted lines is mostly due to changes in B n – B f. Difference between dotted and solid lines is due to collective effects. ≈ 7100 Preliminary Figure courtesy of D. A. Mayorov.

Consider a deformed nucleus. It will have some number of states above the fission saddle point.

Consider a spherical nucleus. It will have many more (rotational) states at the fission saddle point.

P CN decreases substantially with increasing A proj. P CN ≈ 0.5 P CN ≈ 0.25 P CN < 0.1 Preliminary Figure courtesy of D. A. Mayorov.

Changing from 48 Ca to 54 Cr changed the cross section by >7.1  The change in P CN was >5, in line with calculations. A lower cross section would cause this limit to increase. The difference in survivability is  7.8  Of this, only  2 orders of magnitude is due to the change in B n – B f.  (B n – B f )  6 MeV The remainder may be due to collective effects.

The energetics of 54 Cr are much less favorable than 48 Ca. Not surprisingly, there is a strong dependence on the Coulomb parameter z. V.I. Zagrebaev et al.,

The same data as the previous plots. Cross Sections: V.I. Zagrebaev et al.,

The change from 48 Ca to 50 Ti or 54 Cr affects the cross section: Good Things:  cap is flat at best. Slight increase in separator efficiency. Bad Things: Substantial decrease in P CN. Substantial decrease in W sur. (Possibly) slight decrease in beam intensity.

The 248 Cm( 54 Cr, 4n) reaction has three serious problems: A reduction in P CN relative to 248 Cm( 48 Ca, 4n) 292 Lv. (Beam changed from 48 Ca to 54 Cr). The high fissility of the compound nucleus. (Possibly) No increase in survivability due to the predicted closed shell at N = 184. Our data suggests that predictions of  EVR on the order of tens of femtobarns are reasonable. 249 Cf( 50 Ti, 4n) may be more feasible due to a more favorable P CN.

We have used a number of “silver bullets” that have allowed us to create ever heavier elements: Z = (Cold Fusion Reactions): Shell Stabilization Near Z = 108, N = 162. Deformed Products (more on this later). Shell-Stabilized Targets (minor effect). Z = (Warm Fusion Reactions): The neutron-richness of 48 Ca is exceptional among available projectiles. It increases B f and decreases B n. Z > 118 (Warm Fusion Reactions): It is not clear if there is another silver bullet. We may need more beam or another type of reaction.

We will move to odd-Z projectiles in late We will investigate 50 Ti Dy in late We want to move down the periodic table toward transactinides. The K150 is being developed to provide increased intensity for medium-mass beams.

M. C. Alfonso M. E. Bennett D. A. Mayorov T. A. Werke K. Siwek-Wilczyńska and A. V. Karpov for many informative discussions. U.S. DOE Welch Foundation (grant A-1710) Texas A&M University College of Science