Prospects for the Discovery of the Prospects for the Discovery of the Next New ElementNext New Element

C. M. Folden IIICyclotron Institute, Texas A&M University

NN2012, San Antonio, TexasMay 31, 2012

Periodic Table 2012Periodic Table 2012

The heaviest elements are all produced artificially!

The Fission BarrierThe Fission BarrierBf is the fission

barrier.It is caused by a

change in the surface and Coulomb energies at constant volume and density.

40

The Future of Heavy Elements in The Future of Heavy Elements in 19761976

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).

Shell Correction Energies Near Shell Correction Energies Near ZZ = = 108, 108, NN = 162 = 162The reason we

have so many transactinide elements is (partially) due to shell effects.

Evidence:t½(257Rf) = 4.7 s

t½(270Hs) = 3.6 sCross sectionsetc.

A. Sobiczewski and K. Pomorski, Prog. Part. Nucl. Phys. 58, 292 (2007).

Silver BulletsSilver BulletsWe have used a number of “silver bullets”

that have allowed us to create ever heavier elements:

Z = 107-112 (Cold Fusion Reactions):Shell Stabilization Near Z = 108, N = 162.Shell-Stabilized Targets (minor effect).Deformed Products (more on this later).

Shell Effects in SHE ProductionShell Effects in SHE ProductionThe shell effects for Z = 113-118 (warm

fusion reactions) are not as pronounced as for Z = 107-112 (cold fusion reactions).

How do you make a heavy How do you make a heavy nucleus?nucleus?The evaporation

residue cross section can be written as:

*1E

*2E

*3E

1,nS

2,nS

3,nS

1,nE

2,nE

3,nE

4,nS

4,nE

Fission

Fission

Fission

cap CN

cap CN n tot

cap CN n f

( *, )

/

/

x

ii

x

ii

P W E l

P

P

1

1

Detailed Balance and Level DensityDetailed Balance and Level DensityAny 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, 014602 (2005).R. Vandenbosch and J. R. Huizenga, Nuclear Fission (Academic Press, New York, 1973), pp. 227-33.

B

B A A

A B B AA B B A

P PP P

2 2 30 02

0

2

*

*

*/ n

n n

*fff

( )

( )

n

f

E B

nn

E B

f

E B dm gr APP E B K dK

The Canonical ExpansionThe Canonical ExpansionThe level density is a function of energy: (E) Expand around E = E* – Bn and use d(ln

/dE 1/T:

1

n n n n

n n

lnln ( * ) ln ( * ) ( * ) ( * )

ln ( * ) ( ) ln ( * ) /

dE B E B E B E B

dE

E B E B TT

n n( * ) ( * )exp( / )E B E B T

2 2 30 02

0

2

*

*

*/ n

*f

( )

( )

n

f

E B

n nE B

f

E B dm gr A

E B K dK

n f n f/ exp[ ( )/ ]B B T

BBff – – BBnn as a Function of Projectile as a Function of ProjectileThe projectile has a major influence on n/f.

Figure courtesy of D. A. Mayorov.

Better

Worse

Silver BulletsSilver BulletsWe have used a number of “silver bullets”

that have allowed us to create ever heavier elements:

Z = 107-112 (Cold Fusion Reactions):Shell Stabilization Near Z = 108, N = 162.Deformed Products (more on this later).Shell-Stabilized Targets (minor effect).

Z = 113-118 (Warm Fusion Reactions):The neutron-richness of 48Ca is exceptional

among available projectiles. It increases Bf and decreases Bn.

Current and Future History of Current and Future History of Elements Above 118Elements Above 118JINR studied the 244Pu(58Fe, 4n)298120 reaction

and reported an upper limit cross section of 0.4 pb (0.74 pb at 84% confidence).

GSI Experiments:248Cm(54Cr, 4n)298120

Compare with 248Cm(48Ca, 4n)292Lv: EVR 3.3 pb

249Cf(50Ti, 4n)295120 Compare with 249Cf(48Ca, 3n)294118: EVR 0.5 pb

249Bk(50Ti, 4n)295119 (in progess)Other reactions have been proposed:

252Cf(50Ti, 4n)298120238U(64Ni, 4n)298120

4848Ca and Ca and 5454Cr Induced ReactionsCr Induced Reactions162Dy(48Ca, xn)210-xRn 248Cm(48Ca, xn)296-xLv 162Dy(54Cr, xn)216-xTh 248Cm(54Cr, xn)302-x120

Reaction Product NCN Ecm – BCoul E*(CN) E*(CN) – Σ(Bn,i)

162Dy(48Ca, 4n) 206Rn 124 5.5 MeV 48 MeV 15.6 MeV

162Dy(54Cr, 4n) 212Th 126 10.2 MeV 50 MeV 15.8 MeV

248Cm(48Ca, 4n)

292Lv 180 9.6 MeV 41 MeV 15.5 MeV

248Cm(54Cr, 4n) 298120 182 12.3 MeV 43 MeV 15.9 MeV

Column 4 shows the difference Ecm – B, where Ecm 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 Bf, whichever is lower in energy.

Upgraded Capabilities at Texas Upgraded Capabilities at Texas A&MA&MAs part of an upgrade sponsored principally

by DOE, the K150 88” cyclotron is being recommissioned.

http://cyclotron.tamu.edu/facility_upgrade.pdf

Supplied by6.4-GHzECR

Supplied by 14.5-GHz ECR

MARSMARS

Device Acceptance p/p Bmax

MARS 9 msr ±4% 1.8 T mSHIP ~4 msr ±10% 1.2 T mBGS 45 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).

162162Dy(Dy(4848Ca, xn)Ca, xn)210-x210-xRn and Rn and 162162DyDy(54(54Cr, xn)Cr, xn)216-x216-xTh Th Excitation FunctionsExcitation FunctionsDifference

in dotted lines is mostly due to changes in Bn – Bf.

Difference between dotted and solid lines is due to collective effects.

170 175 180 185 190 195 200 205 210 235 240 245 250 255 260

10-4

10-3

10-2

10-1

100

101

102

4n

4n

48Ca + 162Dy206,205Rn

54Cr + 162Dy

212Th

EV

R (m

b)

48Ca or 54Cr Ecot

(MeV)

≈7100

PreliminaryFigure courtesy of D. A. Mayorov.

Collective EffectsCollective EffectsConsider a deformed nucleus. It will have some

number of states above the fission saddle point.

Deformation

FissionNeutronEmission Bf

Bn

V

f} n {

Collective EffectsCollective EffectsConsider a spherical nucleus. It will have many more

(rotational) states at the fission saddle point.

Deformation

FissionNeutronEmission Bf

Bn

V

f} n {

Experimental Experimental PPCNCN Values ValuesPCN decreases substantially with increasing Aproj.

PCN ≈ 0.5

PCN ≈ 0.25

PCN < 0.1

cap surCNP

W

Preliminary

Figure courtesy of D. A. Mayorov.

Summary: Summary: 4848Ca versus Ca versus 5454CrCrChanging from 48Ca to 54Cr changed the cross

section by >7.1 103.

The change in PCN was >5, in line with calculations.

A lower cross section would cause this limit to increase.

The difference in survivability is 7.8 103.Of this, only 2 orders of magnitude is due to the

change in Bn – Bf.

(Bn – Bf) 6 MeVThe remainder may be due to collective effects.

Effects of Effects of BBnn – – BBff and and z z on on Reactions with Odd-Reactions with Odd-ZZ Targets Targets

The energetics of 54Cr are much less favorable than 48Ca.

Not surprisingly, there is a strong dependence on the Coulomb parameter z.

V.I. Zagrebaev et al., http://nrv.jinr.ru/nrv/

Effects of Effects of BBnn – – BBff and and z z on on Reactions with Odd-Reactions with Odd-ZZ Targets Targets zzThe same

data as the previous plots.

Cross Sections: V.I. Zagrebaev et al., http://nrv.jinr.ru/nrv/

Implications for Reactions with Implications for Reactions with Projectiles Heavier Than Projectiles Heavier Than 4848CaCaThe change from 48Ca to 50Ti or 54Cr affects

the cross section:

Good Things:cap is flat at best.Slight increase in separator efficiency.

Bad Things:Substantial decrease in PCN.

Substantial decrease in Wsur.(Possibly) slight decrease in beam intensity.

Implications for the Production of Implications for the Production of Element 120Element 120The 248Cm(54Cr, 4n)298120 reaction has three

serious problems:A reduction in PCN relative to 248Cm(48Ca,

4n)292Lv. (Beam changed from 48Ca to 54Cr).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.

249Cf(50Ti, 4n)295120 may be more feasible due to a more favorable PCN.

Silver BulletsSilver BulletsWe have used a number of “silver bullets” that

have allowed us to create ever heavier elements:Z = 107-112 (Cold Fusion Reactions):

Shell Stabilization Near Z = 108, N = 162.Deformed Products (more on this later).Shell-Stabilized Targets (minor effect).

Z = 113-118 (Warm Fusion Reactions):The neutron-richness of 48Ca is exceptional among

available projectiles. It increases Bf and decreases Bn.

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.

Future WorkFuture WorkWe will move to odd-Z projectiles in late 2012.

We will investigate 50Ti + 162Dy in late 2012.

We want to move down the periodic table toward transactinides.

The K150 is being developed to provide increased intensity for medium-mass beams.

AcknowledgementsAcknowledgementsM. C. AlfonsoM. E. BennettD. A. MayorovT. A. WerkeK. Siwek-Wilczyńska

and A. V. Karpov for many informative discussions.

U.S. DOEWelch Foundation

(grant A-1710)Texas A&M

University College of Science