Cold fusion in symmetric 90Zr-induced reactions

Nuclear Physics ONorth-Holland

A452 (1986) 173-204 Publishing Company

COLD FUSION IN SYMMETRIC J.G. KELLER,

90Zr-INDUCED REACTIONS

K.-H. SCHMIDT, F.P. HESSBERGER, and W. REISDORF

Gesellschaft fCr Schwerionenforschung

Darmstadt,

H.-G. CLERC Institut ftir Kernphysik,

and C-C.

Federal Republic of Germany SAHM

Technische Hochschule Darmstadt, Received

5 September

G. MUNZENBERG

Federal Republic of Germany

1985

Abstract: Excitation functions for evaporation residues were measured for the reactions %Zr +R9 Y, saZr, s2 Zr, %Zr, and 94M~. Deexcitation by y-radiation only was found for the compound nuclei t79Au, t*‘Hg, !“‘Hg and 184Pb. Fusion probabilities as well as fusion-barrier distributions were deduced from the measured cross sections. There are strong nuclear structure effects in subbarrier fusion. For energies far below the fusion barrier the increase of the fusion probabilities with increasing energy is found to be much steeper than predicted by WKB calculations. As a by-product of this work new a-spectroscopic information was obtained for neutron-deficient isotopes between Ir and Pb.

E

NUCLEAR REACTIONS 89 Y, s”.92.96Zr, “Mo(“Zr, xn), E = 321-390 MeV; measured evaporation residue (r above, around, below the fusion barriers; deduced fusion probabilities, barrier distributions. ‘79Au, rso,tE2Hg, ‘s4Pb deduced y-transitions. Enriched targets; velocity filter, parallel-plate avalanche counter, surface-barrier detectors. 178,179.180AU RADIOACTIVITY 172.173.174.175.176.1” 1n ) “5Pt, , ‘*rHg, 1x2 Tl, 181,1R2,1s3Pb( a); measured

E,; deduced

b,.

1. Introduction

The reaction mechanism of cold fusion, i.e. fusion near and below the classical threshold leading to compound nuclei with excitation energies of about 10 to 40 MeV, is interesting in many ways. Both main stages of the process, the formation phase and the deexcitation phase, have been found to lead to rather exciting phenomena: the subbarrier fusion probability has been shown to be strongly correlated with low-energy nuclear structure properties’), and the phenomenon of deexcitation of the formed complete-fusion product by exclusive emission of y-rays, i.e. radiative capture, has been found recently 2, to occur with an unexpectedly large cross section (several tens of pb) in the heavy symmetric system 90Zr + 90Zr. In this work we present an extension of our previous work 2,3) to the systems 90Zr + 89Y, 90,92*96Zr, and “MO. 173

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J. G. Keller et al. / Cold fusion

2

60 -

E

k

*3

w

40

50

60

70

80

90

100

Z CN Fig. 1. Excitation energy E&, at the fusion barrier for symmetric reactions as a function of the nuclear charge of the compound nucleus. The fusion barriers were calculated from the Bass mode14’) (dotted line). For the calculation of the solid line a dynamical hindrance (“extra push’) as calculated from ref.5” ), was taken into account. From all stable target and projectile isotopes the combination leading to the minimum excitation energy was chosen.

Systems in the vicinity of Zr + Zr are expected to lead to particularly low compound-nucleus excitation energies in the vicinity of the fusion threshold (fig. 1). This is due to the favourable reaction Q-values for these systems caused by the superposition of liquid-drop trends, which favour symmetric reactions (for constant total mass), and shell effects (N = 50, Z = 40) in the reacting nuclei. On the other hand, one can expect for these systems reasonably large evaporation-residue cross sections near the fusion threshold mainly for two reasons: (i) The fission barrier heights of the formed mercury-like nuclei are still comparable to typical

energies

required

for particle

evaporation.

Thisis in contrast

to the

situation in the cold-fusion reactions that have been used recently for the synthesis of the highly-fissile heavy elements 4). (ii) The effective entrance-channel fissilities5) of these systems are just at the borderline of the region beyond which strong dynamical hindrances to the complete-fusion process have been observed: as an example, we mention the observation by Sahm and coworkers 6, of dynamical increases of fusion barriers (“extra-push energies”) of about 20 MeV for the system Sn + Zr. Another reason that makes fusion studies of the systems around Zr + Zr attractive, is connected with the well-known, rapidly-varying nuclear-structure properties in the vicinity of (Z, N) = (40,SO) and hence with the expectation that this will strongly influence the threshold behaviour of the fusion process. Studies with similar heavy systems that support this expectation have been published by Beckerman et al. 7, and Reisdorf et al. ‘).

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J.A. Keller et al. / Cold fusion

In this work we have used the velocity from the 90Zr projectiles behind

SHIP

allowed

accelerated

filter SHIP 9, to separate

by the UNILAC

us to take advantage

fusion products

at GSI. The detector

of the a-activity

system

of most of the isotopes

formed in the fusion reactions studied here, by using the half-lives, mother-daughter relations and characteristic a-energies for the identification of individual nuclides in addition to a low-resolution kinematic identification of the ensemble of fusion products. In particular, we were able to confirm the phenomenon of radiative capture for at least three more systems [in addition to 90Zr + 90Zr, ref. *)I. Excitation functions for this process, as well as for many of the individual fusion products, could also be determined. The high sensitivity of SHIP made it possible to measure total evaporation-residue (ER) excitation functions down to the 100 nb level. In sect. 2 we present the experimental method in more detail. As a by-product of this work we could obtain new Lu-spectroscopic information for light isotopes in the region Ir to Pb. This is summarized in sect. 3. The measured evaporation-residue cross sections are presented in sect. 4. The discussion involves both the formation and the deexcitation stage of the reaction studied. Starting with the latter, the data are confronted in subsects. 5.1-5.4 with extensive calculations using evaporation theory. Our interest was focussed on the following questions: Can the measured radiative-capture cross sections be understood in the framework of the statistical model of compound-nucleus deexcitation? Can this model also describe the other (xn,pxn, axn) excitation functions? What are the fission barriers required to reproduce the data and how well do they compare with theoretical expectations and known systematics? Concerning the formation aspect, we present in subsect. 6.1 a method to extract fusion probabilities from our data and discuss the results in terms of current models for subbarrier fusion (subsect. 6.2). An interpretation of the fusion excitation functions in terms of barrier penetrabilities, barrier shifts and barrier distributions is given in subsect. 6.3. Our conclusions are drawn in sect. 7.

2. Experimental

method

The experiments were performed at the velocity filter SHIP 9, at GSI, Darmstadt. Thin targets (loo-250 pg/cm*) of 89Y, 90Zr, 92Zr, 96Zr and 94Mo were bombarded with a 90Zr beam. The targets of 90Zr and 92Zr as well as the target material of 94Mo were produced at the mass separator SIDONIE of the Laboratoire RenC Bernas in Orsay. The target of 96Zr was produced at the target laboratory at GSI from isotopically-enriched (85.25% 96Zr) material. A schematical drawing of the experimental set-up is shown in fig. 2. The target thicknesses and the beam currents as well as the beam-energy distributions were monitored by detecting the elastically scattered projectiles at an angle of 30” with two surface-barrier detectors with diameters of 10 mm and 18 mm positioned at the right- and at the left-hand side of the beam at distances of 703 mm and 460 mm,

176

J. G. Keller et al. / Cold&ion

detector system

velocit filter SIJP

PPAC stop

monitor

-7 beam catcher

analog and digital pulse 3 processing

I

kinematic analysis

L-l

4

\1 N,. Nt,

-2,

-A, position

E k&m

Fig.

2. The

experimental

setup.

The measurable parameters

quantities as well as their are shown.

4’ Z, A

connection

to derived

respectively. A carbon foil with a thickness of 30 pg/cm2 was positioned 69 cm downstream from the target to reestablish the equilibrium ionic-charge distribution. Carbon foils of 35, 55 and 180 pg/cm2 were used to vary the beam energy in small steps. The 180 pg/cm2 degrader was used only at energies above the fusion barrier. The velocity filter SHIP accepts products within a 20% energy and ionic-charge window in a forward cone of f 1.5” [ref? )]. For the detection of evaporation residues behind SHIP we used a detector telescope

consisting

of a 70 x 50 mm* position-sensitive

parallel-plate

avalanche

counter (PPAC)“) followed 25 cm downstream by two concentric surface-barrier detectors into which the products were implanted. The central solid-state detector had an active area of 450 mm2 and the outer ring detector had an area of 1550 mm*. Individual evaporation channels were identified by their characteristic a-decay. The a-energy resolution was 25 keV (FWHM) and 50 keV in the ring detector.

2.1. MONITORING

in the central

surface-barrier

detector,

OF THE BEAM ENERGY

In order to determine strongly energy-dependent cross sections it is necessary to monitor the incident beam energy with high accuracy. We measured the arrival time of elastically-scattered particles at the monitor detector relative to the pulse frequency (27 MHz) of the accelerator. For this purpose the small detector at 703 mm distance

J.G. Keller et al. / Cold fusion

111

from the target was used. Thus the time-of-flight of the projectiles was determined for the 45 m flight path from the exit of the accelerator to the detector with an accuracy of 0.5 ns, mainly limited by the finite size of the beam bunches. The energy distribution of the beam as well as the change of the mean energy between two energy settings of the UNILAC could be determined with an accuracy better than 300 keV (0.07%). The absolute beam energy was measured separately. The error in the beam-energy scale amounted to 500 keV [ref. ‘l)].

2.2. IDENTIFICATION

OF EVAPORATION

RESIDUES

While scattered projectiles and backscattered target particles are suppressed very efficiently by SHIP in asymmetric reactions, the suppression becomes poorer when the velocity of the evaporation residues is closer to the velocity of the beam’). In the present experiment the background rate in the detector telescope behind SHIP, which is due to scattered projectiles and recoiling target nuclei, amounted to about 1 kHz. The detection limit for evaporation residues is determined by the pile-up of these background pulses, since the total energy as well as the total nuclear charge in the pile-up of two scattered projectiles is the same as for a true evaporation residue. A hardware pile-up-rejection unit was used to suppress pulses with time distances between 20 ns and 2 ps. Furthermore a large portion of the pile-up events not rejected by the pile-up hardware unit could be recognized in a AE-E plot. The E signal from the stop detector as well as the A E signal from the PPAC, are somewhat larger for pile-up events than for evaporation residues. This is due to the pulse-height defect in the high-resistivity surface-barrier stop detectors (E-signal), and to the

1oi

0

I

’

I

0

I

1

scattered projectiles 5 1.........*.. ..,I... 0 _ 51’

,,..

-5 -

100

‘4

...-.

““‘i

beam

up

g”zr+g6zr

‘:i’

I

50

I

P

(3.6

evaporation

1

primary

+pile

,.I,... .,,I,. ..0 .

I

I

residues

I

150

I

I 200

I

MeV/u)

I 250

I

I

I

300

Energy (MeV) Fig. 3. Two-dimensional plot of the TOF between the parallel-plate avalanche counter and the stop detector behind SHIP and the energy deposited in the Si stop detector. The size of the clusters is proportional to the log of the counting rate per channel. The number of evaporation residues in this example corresponds to a cross section of 9 pb. Events in the region encompassed by the polygon have been identified as pile-up events on the basis of their position in a two-dimensional A E-E plot (not shown in the figure).

J. G.Keller et al. / Cold fusion

178

5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4

E, (MeV) Fig. 4. a-energy spectrum of evaporation residues implanted into the central stop detector for the reaction WZr(4.02 MeV/u) + %Zr. The numbers in the insert indicate the number of the implanted nuclei (before a-decay) for the different nuclides as determined from the a-energy spectrum together with information about a/EC branching ratios.

nonlinear Z dependence of the A E signal. The counts identified way are marked in a two-dimensional TOF-E plot (fig. 3).

2.3. IDENTIFICATION

OF SINGLE

EVAPORATION

as pile-up

in that

CHANNELS

In order to evaluate the primary population rates for specific evaporation channels, the information of the measured a-spectra was used together with known branching ratios and a-decay energies of all a-emitting nuclei produced directly or populated as decay products. Also the number of evaporation residues registered by the detector telescope (see subsect. 2.2) was used. This is described in more detail in ref. 12). For illustration purposes, fig. 4 shows an a-spectrum as registered in the central detector.

2.4. DETERMINATION

OF ABSOLUTE

CROSS

SECTIONS

The cross sections are normalized to the cross sections for Rutherford scattering. In order to average over the oscillations in the Mott scattering cross section for reactions with identical beam and target nuclides, one of the two Rutherford monitors had a solid angle of 2.3” covering about three fluctuation periods of the Mott scattering cross section. As mentioned earlier, the other detector was used to monitor the exact position and angle of the beam.

J. G. Keller et al. / Cold fusion

The

transmission

of SHIP,

which

is in general

179

different

channel, was calculated by a Monte Carlo program. evaporated isotropically; the angular scattering

for each evaporation

All particles are assumed to be was calculated according to

Eastham13), the energy loss according to Braune and Schwalm14), and the energy-loss straggling was taken from Hvelplund”). The ionic-charge distribution was taken from Nikolaev et al. 16). The Monte Carlo program was adjusted 12) to reproduce transmission measurements from refs. “,l’). In the reaction 90Zr + 96Zr individual evaporation channels could not be separated because the ol-branching ratios are too small. In order to evaluate the mean transmission, the division of the total evaporation cross section into single evaporation channels was calculated by an evaporation code. The information from the cross sections measured for the neighbouring parameters of these calculations.

systems

has been used to adjust

the

3. spectroscopy The spectroscopy of the nuclei produced in the reactions presented here are not the main topic of this paper. However, a knowledge of the spectroscopic properties is essential for evaluating the cross sections for different deexcitation channels from the measured a-spectra.

3.1. ASSIGNMENT

OF NEW (r-LINES

It was possible cross-bombardments

to identify some new cy-lines. The identification was based on as well as on a comparison of excitation functions for several

a-lines or, whenever possible, by mother-daughter correlations. The methods and the reactions used for the identification are indicated in table 1. For isotopes for which no a-decay was known previously, the measured decay energies

are in good agreement

with predictions

of the Viola systematics19).

TABLE 1 New a-lines Nuclide “‘AU ‘“‘Au ,x*Tl lxlPb ‘s2 Pb IX3Pb Is3 Pb “) Assignment b, Assignment

EL% 5850(20) 5685(10) 6406(10) 7211(10) 6921(10) 6873(10) 6580(10)

“) “) “) b, b, b, b,

based on excitation functions. based on mother-daughter correlations.

Etheo n

Target

5910 5671 6406 7197 7071 6945 6945

*‘Y “Zr y2 Zr,’ 94M~ 94 MO 94MO y4 MO 94 MO y4 MO

180

J.G. Keller et al. / Cold fusion

In the reaction WZr + 94Mo + lE4Pb* the a-spectra were found to be very complex. It was not possible to assign all o-lines unambiguously. In particular there are indications for a-lines in the range between 5.8 and 6 MeV, probably originating from the nuclei ‘*‘Tl and i**Tl.

3.2. EVALUATION

OF TOTAL

(1 VERSUS

(EC + p’)

BRANCHING

RATIOS

By comparing the results for the reactions s”Zr + WZr, 92Zr, *‘Y some total a-branching ratios could be determined for the first time. In other cases, previously known values were remeasured with better precision. For the evaluation two methods were used. The first, more common one, is to calculate the branching ratio from the population rate by radioactive decay of the mother nuclide and the a-decay rate of the daughter. This method is only useful for isotopes which cannot be produced directly in the reaction. The population of the nuclide under consideration by electron capture or /3’ decay has to be taken into account, too. The spectroscopy of the two possible mother nuclides has to be known in this case. For isotopes fed directly in the reaction, only a lower limit for the total (Y branching can be set by this method. This was the case for the isotopes 17*Auand ‘*‘Au. The second method needs as an essential input the spectroscopic properties of all other isotopes populated directly or, instead, the properties of the daughter nuclides of these isotopes. In this case the primary population of the isotope under considera-

TABLE 2 Total a-branching Nuclide

E, WV1

p (1

pt.

ratios measured lit

LI

b’o’, oi

here

thee

h’“’ 01 calculated

from

0.44

‘7sAU

5920,598O

lT9Au

5848

2 0.40

’ “Au

5685

“5Pt

5964,6038

0.573(11)

173Ir

5665

0.0202(8)

0.32 0.055

0.220(9)

0.29

> 0.018

0.069 0.75(15)

0.79

1741r

5478

0.0047(27)

‘751r

5393

0.0085(28)

0.047

‘76 Ir

5118

0.021(4)

0.0022

“‘Ir

5011

0.0013(7)

0.0014

Symbols: b, - total a-branching. X, - sum of all a-decays observed. residues, z e.r - sum of all evaporation residues from other channels x rest - sum of all evaporation

as calculated

from the n-spectra.

J. G. Keller et al. / Cold fusion

181

tion can be calculated as the difference between the measured total rate of evaporation residues and the rate of evaporation residues from other channels, evaluated from the a-spectrum. This method will only work in a proper way if the nuclide under consideration represents one of the dominant channels. It was used for the isotope ‘79Au. The results are listed in table 2. The method used for the evaluation is indicated. For comparison the theoretical values are also listed. Partial a-halflives were calculated according to Rasmussen2’), and the halflives for EC or p’ were calculated from the “gross theory” of Takahashi et aZ.21) using the mass tables of Moller and Nix 22). When calculating the partial cY-halflivesthe highest known a-energy was used. No hindrance from spin or other specific spectroscopic properties was taken into account.

3.3. RELATIVE INTENSITIES OF DIFFERENT a-LINES BELONGING TO THE SAME NUCLIDE

For the evaluation of cross sections it is necessary to know the branching ratios for the different cY-linesof one nuclide. HeBberger 23) showed that branching ratios for cw-lines of nuclei implanted into a surface-barrier detector can differ from the results of measurements by catcher techniques if a-transitions to low-lying levels in the daughter nucleus are present which decay by strongly-converted transitions. In this case the conversion electrons may also be stopped in the surface-barrier detector and the measured sum-energy of the a-particle and the conversion electron agrees approximately with the energy of the transition to the ground state. The detection efficiency for these electrons depends on the implantation depth, on their energy, and on the detector thickness; in this experiment electrons with energies up to 300 keV could be stopped with an efficiency of 50%. Therefore the branching ratios evaluated from these data can only partially be compared with data measured by other techniques. All spectroscopic data used in this work are listed in table 3. For nuclides for which the spectroscopic information used here differs in some respects from previously published values also the original reference is given.

4. Measured evaporation-residue cross sections The measured cross sections for specific deexcitation channels in the reactions 90Zr + 89Y, 90,92Zr and %Mo are evaluated according to the method described in subsect. 2.3 and ref.12). In nearly all cases nuclides produced by evaporation of charged particles are also populated indirectly by (Yor by /3+/EC decay. Therefore cross sections of channels corresponding to proton or a-particle evaporation could not be determined in all cases.

J. G. Keller et al. / Cold fusion

182

TABLE 3

Spectroscopic Nuclide

E, [keV]

(1 -h,)

“OOS

5405 5240 5105 4940 4760 6110 5180 5665 5478 5393 5118 5011 6213 6035 5964 6038 5757 5528 5527 5458 5302 5150 5194 5139 5020 4840 4730 6737 6546 6626 6435 6290 6260 6150 6115 5920 5980 5850

0.120 0.0103 0.003 0.0002 0.0@32 0.8300 = 0.0300 0.0202 0.0047

“‘OS t7* OS “)OS ‘74Os ‘69Ir ‘721r “‘Ir “4Ir ‘751r i’6Ir “‘Ir “3Pt ‘74Pt “5Pt “6Pt “‘Pt “UPt “9Pt t’sPt b) *sopt ‘s’ Pt Is2 Pt *s3 Pt “3AU “4AU

“‘Au ’ “Au

0.0085 0.021 0.0013 0.84 0.83 0.573 0.573 0.403 0.403 0.052 0.074 0.074 0.0021 0.0027 0.003 00306 o.OQO2 o.OOcO13 1.00 1.00 1.00 0.95 1.00 1.00 1.00 1.00 0.40 0.40 0.40

b, 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 LOO 1.00 1.00 1.00 1.00 1.00 0.748 0.252 0.986 0.014 l.OQ 0.9945 0.0055 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.70 0.30 1.00 0.20 0.80 0.35 0.65 0.659 0.235 0.106

properties

used in this work

Ref.

iuclide

E,, [keV]

Ens78 HaH79 LeS78 LeS78 LeS78 Sne83 Sne83, “) LeS78, “) LeS78, “) LeS78, “) LeS78, “) LeS78, “) HaH79 HaH79 HaH79 HaH79. “) HaH79 LeS78 HaH79 HaH79 HaH79 L&78 HaH79 LeS78 LeS78 LeS78 LeS.78 Sne83 Sne83 Sne83 CaD75 LeS78 LeS78 LeS78 LeS78 LeS78,“) LeS78.“) “)

‘79Au “‘Au “‘Au

5685 5623

tXZAu “‘Au ‘s4Au “5Hg 176Hg i”Hg “sHg “VHg ‘a” Hg ‘*‘Hg

‘s>Hg

tXITlb) tx*Tl ‘H)n IH4D 1Rqlb) “‘Pb ix2Pb “*Pbh) iX?Pb

IX4Pb

b,

Ref

6340 6162 5988

1.00 1.00 1.00 0.84 0.504 0.458 0.32 0.32 0.32 0.32 0.155 0.155 0.12 0.12 0.013 0.013 1.00 1.00 1.00 0.021 0.021

1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.647 0.353 1.00 1.00 1.00 1.00 1.00 1.00 0.8095 0.0536 0.0672 0.0696 0.996 0.004 0.953 0.047 0.996 0.004 1.00 1.00 1.00 1.00 1.00

LeS78, “) “) LeS78 LeS78 SeE81 LeS78 LeS78 LeS78 LeS78 Sne83 Sne83 LeS78 LeS78 Sne83, Hes82 Sne83, Hes82 LeS78. “) LeS78. “) LeS78, “) HaH79, “) HaH79 LeS78 HaH79 LeS78 LeS78 LeS78 Sne83 “) Mat78 LeS78 LeS78

7211 6868 6921 6720 6792 6873 6580 6630

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1 .oo

1.00 1.00 1.00 0.784 0.171 0.011 0.034 1.00

“) Sne83 “) SrT80, “) SrTEO.“) “) “) SrT80

5353 5460 5343 5172 5108 6878 6767 6580 6425 6288 6120 6003 5920 6071 6134 5865

‘X’Hg IX4Hg

(1 -b,)

5535 5380 6566

0.220 0.018 0.011 0.011 o.Oinl4 0.0004 0.0030 0.00022

References: “) This work. b, Probably isomeric state. CaD75-C. Cabot, C. Deprun, H. Gauvin, B. Lagarde, Y. Le Beyec and M. Lefort, Nucl. Phys. A241 (1975) 341. Ens78 - H.A. Enge, M. Salomaa, A. Sperduto, J. Ball, W. Schier and A. Graue, Phys. Rev. C25 (1978) 1830. HaH79 - E. Hagberg, P.G. Hansen, P. HornshoJ, B. Jonson, S. Mattsson and P. TidemandPetersson Nucl. Phys. A318 (1979) 29. Hes82 - F.P. HeBberger, GSI annual report 1982 (Darmstadt, 1983) p. 64. LeS78 - C.M. Lederer and VS. Shirley, ed., Tables of isotopes 7th ed. (Wiley, New York, 1978). Mat78 - S. Mattsson, thesis, Gijteborg (1978) unpublished. Sne83 - J. Schneider, thesis, Maina (1983). GSI report GSI-84-3. SrT80 - H.J. Schrewe, P. Tidemand-Petersson, G.M. Gowdy, R. Kirchner 0. Klepper, A. Plochocki, W. Reisdorf, E. Roeckl, J.L. Wood, J. Zyliu, R. Fass and D. Schardt, Phys. Lett. 91B (1980) 46.

J. G. Keller et al. / Cold fusion

183

TABLE4

Total evaporation Reaction

EC m [MeVl”)

90Zr +xy Y

168.72 169.66 170.55 171.08 172.71 174.42 174.90 175.00 177.07 178.52 180.45 183.61 183.68 186.42 191.66

“Zr

172.08 173.57 174.41

+‘O Zr

174.90 175.59 175.80 175.95 176.42 176.91 177.81 180.09 181.06 183.47 184.99 187.56 189.85 193.68 195.74

residue cross sections Reaction

eb) 344 5.14 83.1 290 2.21 7.41 8.15 8.04 15.5 25.9 24.2 28.7 30.4 49.1 40.5 81.3

nb + pb k pb+ pb * mb f mb i mb + mb k mb+ mb + mb + mb + mb k mb & mb i

19% 14% 12% 10% 10% 10% 10% 10% 12% 10% 10% 10% 13% 10% 12%

/.rb t_ pb & pb+ pb k jrbi pb k pb_+ mb * mb + mb & mb k mb_+ mb + mbi mb k

10% 8% 8% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

eb)

IZr +92 Zr

169.60 170.10 171.01 171.50 173.37 174.25 175.44 177.33 177.80 179.88 182.05 183.30 186.45 187.06 189.12 192.31 195.19 198.48

121 589 6.01 14.3 72.4 156 463 1.57 1.80 4.13 7.56 7.88 9.78 16.3 22.6 13.3 28.4 14.4

oZr +96 Zr

166.29 167.22 168.35 168.86 169.79 172.15 174.52 176.86 179.17 181.59 183.82 187.26 190.68 196.77 203.16

3.46 pb f 10% 9.56 pb + 10% 19.5 pb & 10% 36.3 /rb i 10% 109 pb k 10% 323 pb& 10% 1.53 mb & 10% 3.12 mb & 10% 5.85 mb t 10% 9.40 mb k 13% 14.4 mb & 16% 19.3 mb f 21% 23.7 mb + 25% 28.5 mb f 32% 22.5 mb + 37%

“Zr +94 MO

179.30 181.36 182.27 183.70 184.57 187.70 193.61 200.32

148 2.51 4.13 16.6 19.0 131 429

nb + 230%/83%/ 613 nbt 19% 2.59 pb + 10% 12.6 58.3 68.6 125 132 252 594 2.55 3.03 4.71 7.62 10.3 6.99 15.1 9.63

EC,, [MeV] “)

nb *42% nbk26% j_rb i 7% pb f 9% /rb i 10% pb+ 10% /rbk 10% mb & 10% mb i 10% mb * 10% mb f 10% mb + 10% mb & 10% mb i 10% mb & 11% mb + 10% mb + 11% mb f 10%

nb& 24% pb + 10% pb k 10% pb & 14% pb + 15% pbk 11% pbkll%

1.12 mb k 12%

“) The absolute uncertainty of the beam-energy scale is about 500 keV (lab)“). Relative to each other the energies are accurate to better than 300 keV. The energies listed are corrected for the target thickness and for the measured beam-energy distribution. b, The errors include statistical errors as well as uncertainties in the transmission of SHIP arising from uncertainties in the distribution of the total cross sections on the different evaporation channels.

184

J.G. Keller et al. / Cold fusion

Because of the unknown spectroscopic properties of the thallium isotopes, no cross sections for (Y-and p-channels could be determined in the reaction 90Zr + 94Mo. The total evaporation-residue cross sections are given in table 4. The errors include uncertainties of the calculated transmission of SHIP caused by the fraction of evaporation residues which cannot be assigned to a definite channel because of their small a-branchings. The data have been taken in two separate runs. While the cross sections for the xn and p, xn channels are consistent within the given errors, the total evaporationresidue cross sections for energies above the fusion threshold are different for the two runs. The transmission of charged-particle channels such as 2axn or cYpxn, where the angular distribution as well as the velocity distribution of the evaporation residues is peaked outside the acceptance of SHIP, is very sensitive to the exact beam setting. We think that the deviation between the two runs is caused by this fact.

5. Discussion of evaporation-residue cross sections 5.1. EVAPORATION

CALCULATIONS

Within the statistical model the formation of an evaporation residue is divided into two steps: the formation of the compound nucleus and its deexcitation. The formation process and its energy dependence is discussed in sect. 6. The results given there were used to define the primary population of compound nuclei. The parameters of the deexcitation process will be discussed here. For the calculations we used the evaporation code HIVAP 24). The ground-state masses and particle separation energies of the nuclei involved here have been taken from the tables of Liran and Zeldes “), or, if possible, from the experimental values reported in ref. 26). The ground-state shell effects are small and therefore not very important in the evaporation calculation. They were determined from the differences between the experimental value - or the value from ref. 25) - and the liquid-drop-model mass prediction 27). The transmission coefficients for particle evaporation are calculated in the WKB approximation. The parameters of the potentials used were fitted to measured cross sections

for the capture

of neutrons,

protons

and a-particles.

in ref. 28). For the y-deexcitation

Their values are given

only El and E2 transitions were taken into account. The y-decay width for statistical El and E2 transitions was calculated according to the formula

dr,EL( E,, j, E,

j’) =

P(E-E,A)

185

J.G. Keller et al. / Cold furion

with E, the y-energy, j the angular momentum of the final state, L the multipolarity of the transition, and E and j’ the energy and angular momentum of the initial state. The quantity CL is an adjustable parameter, and rsL are the well-known Weisskopf estimates 29)

rE2 & = 4.9 x 10-‘4A4’3

(5.3)

Alternatively, the El strength derived from the giant-dipole resonance (GDR) was used. In this case the width I’, [ref. 30)] is given by

dr,( E,, j, E, 7) =

@-%

j)

C.A

P(E, j’)

r,

Ey”

@ '@(E;-E;)~+E~~$

dE,,

(5.4)

with Egi and rti the energy and width of the GDR, and A, the mass number of the nucleus. For the energy- and angular-momentum-dependent level density the formula for a Fermi gas consisting of two kinds of fermions 30) was used:

&W)=*

,E_f!~f~~c~ ,exp[2~a(E-(A2/2e)j(j+l))]. +

1)l

(5.5) The moment of inertia 8 and the level-density parameter a are different for the ground state and for the saddle point. The moments of inertia are calculated from the rotating-liquid-drop model 31); the asymptotic values for a, and a, are given by a macroscopic description24) which is similar to the description of ref. 32). Groundstate shell effects were taken into account according to ref. 33). The fission barriers are not very well known for neutron-deficient isotopes around mercury. Therefore they are used as fit parameters in order to reproduce the measured cross sections at energies above the fusion barrier. The isospin dependence of the fission barrier was taken from the empirical description of ref. 34) which differs from the predictions of ref.31). Shell effects at the saddle point have been neglected.

5.2. RADIATIVE

CAPTURE

In all reactions investigated here in which single evaporation channels could be separated by use of a-spectra, the ground-state a-decay of the compound nucleus was observed 2). Obviously the only way of cooling in these cases is the emission of y-rays. The cross section for this process is found to vary from system to system: it is maximal in the reaction 90Zr +90Zr and a factor of about 25 smaller in the reaction

186

J. G. Keller ei al. / Cold fusion

Fig. 5. Part of the chart of nuclides. The solid lines indicate where the neutron binding energy B, is equal to either the fission barrier B, or the sum Sn of the proton binding energy and the Coulomb barrier against proton emission. These lines indicate roughly the borders between the regions of predominating neutron evaporation, proton evaporation, or compound-nucleus fission. The compound nuclei under consideration are marked by circles.

WZr + 94Mo (table 4, fig. 8). These differences can be understood when taking into account the different excitation energies at the fusion barrier and the different fission barriers of the systems. The mechanism of radiative capture is well known from neutron- and protoncapture reactions. In analogy to electron capture in atomic physics, this process is interpreted as a direct process which is accompanied by the emission of a single y-ray from the giant-dipole resonance. It is quite doubtful that the mechanism here is the same, since during the fusion process the two zirconium nuclei undergo a rather complex shape evolution. Nevertheless, we use the term “radiative capture” also for the process investigated here. The radiative capture which could be observed in these reactions with cross sections up to 50 pb is probably favoured by the high threshold energies for other processes: for nuclides around 18’Hg the fission barriers, the neutron binding energies as well as the sum of binding energy and Coulomb barrier for protons are = 10 MeV (fig. 5). Since the fusion barriers are small in terms of excitation energy, it was possible to reach very low energies - down to E * = 12 MeV in the system 90Zr + 94Mo. Therefore it is not so surprising to find radiative capture (y-channel) as the dominant deexcitation process for such low excitation energies. It is, however,

J. G. Keller et al. /

Coldfusion

187

Fig. 6. Excitation functions for the xn cross sections measured in reaction WZr + 90Zr. The solid lines are the result of a HIVAP calculation with the giant-dipole El strength Cs fitted in order to reproduce the measured ratio uJqn.

more surprising to observe the y-channel also at much higher excitation energies with fairly large cross sections. For example, in the system 90Zr + 90Zr the cross section for the y-channel is measured to be about 10 pb at an excitation energy of 27 MeV in the compound nucleus. In the framework of the statistical model the cross section for radiative capture is mainly determined by the El strength. Evaporation calculations with the code HIVAP

showed

that the El strength

could be determined

by a fit to the ratio of the

cross sections for the y-channel and the In channel, since this ratio was found to be rather insensitive to the fission barriers as well as to the fusion probability. In the last few years the excited-state giant dipole resonance (ESGDR) was the object of an intensive research. Measurement of (p, y) reactions on calcium have shown that the width of the ESGDR is increasing with increasing excitation energy 35). An analysis of high-energy y-rays in reactions like 12C + 154Sm + 166Er* (E * = 54 MeV) indicates that shape, position and width of the ESGDR are similar to the parameters known from the El giant-dipole resonance built on the ground state (GDR) 36). Lacking more detailed information we used the standard parameters of an unsplit resonance 37*38) as a starting point. However, a calculation performed with these parameters (Fti = 5 MeV, C. = 1.127 x 10e6, E, = 80 the ratio ~,./a,, is underMeV/A c113)) did not reproduce the data. In particular estimated by an order of magnitude. Usually it is required that the El strength satisfies the El sum rule, and this limits the parameter Cpi in eq. (5.4). However, the y-strength may locally be higher for y’s

J. G.Keller et al. / Cold fusion

188

TABLE

Fitted parameters Compound nucleus ‘19Au ‘*‘Hg ‘s*Hg ls4Pb

Csi/Cz’

10.61 11.25 9.94 11.33

9.94 8.45 9.59 5.84

5

of the evaporation

3.9 4.6 3.5 9.2

[MeV]

k f + f

0.6 0.5 0.4 0.9

calculations

Eti [MeV]

C& [MeV-‘1

14.20 14.17 14.12 14.07

11*2 lo* 1 12* 1 751

b,

0.015(5) 0.020(2) 0.015(2) 0.040(5)

“) Calculated from the mass tables of Wapstra, Bos 26) or Liran, Zeldes 25). b, For definition of C,,, see eqs. (5.1) and (5.6).

in the region between 3 and 8 MeV which is important for the radiative capture 39,40). A change of Cti can also be interpreted as a change of the level density in the daughter nucleus by the same amount. Responsible for that may be an unrealistic energy dependence of the level density when comparing the level density after neutron emission (B, = 10 MeV + E * = 8 MeV) with the level density after emission of one y of e.g. 6 MeV ( -+ E * = 14 MeV from a nucleus with E * = 20 MeV). A considerable uncertainty is caused by the unknown Q-value of the reaction because the binding energy of ‘so Hg is not known experimentally and was therefore taken from a semiempirical descriptionz5). A fit of the parameters of the y-strength function should be allowed, if the parameters are interpreted as effective parameters. It is possible to obtain a reasonable fit of the measured excitation functions by changing one of the two parameters C, or Eti, while keeping the other parameter fixed at the values given in the literature. The fitted values for Cti or Egi deviate drastically from those given in ref.38 ), and they vary strongly from system to system, see table 5. Furthermore the measured shapes of the excitation functions are not reproduced for all systems: in the calculations the maxima of the excitation functions are too sharp, and the fall-off to higher energies is less steep than that of the data. An example is shown in fig. 6. For comparison we also used the El strength derived from eq. (5.1) with the constant 41) c,, = c;,(2j

+ 1).

(5.6)

The values which fit the data are also given in table 6. It is possible to describe the excitation functions fairly accurately (fig. 7) but again the strength varies strongly from system to system. However, the results of the evaporation calculation were found to depend strongly on the insufficiently known masses of the fusion products as well as on the detailed description of the level density at low excitation energy.

J.G. K&r

ef al. / Cold fusion

189

10-2 10-3 10-" g n

1o-5 lo+ 1O-7 10-* 10-9

1o-2 1o-3 10-&

*.

_a

,I

s? 1o-5 Q lo-"

n

1o-7 lO-8 1o-g

I

90Zr + 89y

I

1

1

I

I

I

15

20

25

30

35

40

E” (MeV1

45

10

15

20

25

30

35

40

E” (MeVl

Fig. 7. xn cross sections for aII systems under consideration. For the calculations (solid lines) the y-width of eqs. (5.1) and (5.6) was used.

It would be interesting to compare the recently measured y-spectra for radiative capture in the reaction ??,r + %Zr + lsoHg [ref. 39)] with the results of statisticalmodel calculations. This will be the subject of a forthcoming paper @). In order to determine all other parameters of the evaporation calculations, such as fission barriers and the population of the compound nucleus p(E, Z), the El strength derived from eqs. (5.1) and (5.6) was used with the parameters C& as listed in table 5.

5.3. CHARGED-PARTICLE

EVAPORATION

When comparing the measured cross sections for evaporation residues formed by the evaporation of protons or cx-particles with the results of the evaporation

J.G. Keller et at./ Cotdfusion

190

B

I rg --

:

wn

:."lp,2n

g

lo-@10-7

,..‘f

_

?A Q

10-3 10-L 3 10". r) 10" 10-7 10"

10-2

0 - lo A - lo,ln

10*

10,ln /

/I

gOZr + gOZr 15

la,2n

I

,

I

I

I

20

25

30

35

40

E’ (MeV) Fig. 8. Excitation functions of p xn, 2p xn and axn channels for the systems %Zr +90 Zr -PO Hg. The parameters used for the evaporation calculation (solid lines) are the same as in fig. 7. The cross sections for the la channel include also the 2p, 2n channel.

J.G. Keller

calculation

performed

with the same parameters

the 2p channels

are reproduced

p, xn channels

are overestimated,

factor

of 5-50

et al. / Cold fusion

depending

191

which fit the xn cross sections,

within the errors. An example and the axn

channels

on the system. The deviation

only

is shown in fig. 8. The

are underestimated

is increasing

by a

with decreasing

fission competition. Similar deviations between experiment and calculations were also found for the system Ar + Hf [ref. “)I and Sn + Zr [ref. 42)]. Possibly, one reason for these deviations can also be found in the energy or angular-momentum dependence of the level density, as proposed to explain the radiative-capture cross sections. Another reason may be the transmission coefficients for charged-particle emission, which may differ from those for the inverse reactions.

5.4. FISSION

COMPETITION

Only very few fission barriers have been measured in the region of neutron-deficient nuclides. Therefore it is necessary to use model predictions for the fission barriers. Dahlinger and coworkers 34) showed that current models for the calculation of the liquid-drop part B:.d. of the fission barrier, B f = B’.d.f

6M g + 6M St

with SMg and 6M, being the shell correction at the ground state and at the saddle point, respectively, are not able to reproduce the data as a function of the asymmetry I = (N - Z)/A. Therefore the liquid-drop fission barriers entering into the evaporation calculations have been treated as free parameters in the evaporation calculations and were adjusted to some extent in order to fit the data. In table 6 our data on fission barriers are compared with several theoretical estimates.

It should be noted that our data are sensitive

to the fission barriers

angular-momentum range up to 30A. The angular-momentum fission barriers was taken from ref. 31).

dependence

in the of the

TABLE 6

Comparison

of the fitted fission barriers

to model predictions

Fission barrier Nuclide

exp.

‘19Au 180H g i**Hg ls6Hg lX4Pb “) Calculated b, Calculated ‘) Calculated

10.1 8.5 9.6 10.5 5.6 according according according

& 5% + 5% k 5% * 5% k 5%

[MeV]

“)

b,

‘)

11.6 10.2 10.9 12.0 8.2

12.1 10.8 11.4 12.5 8.8

17.5 15.7 16.1 16.6 12.9

to the finite-range liquid-drop to the liquid-drop of ref.*’ ). to the droplet model 59).

model 44).

J. G.Keller et al. / Cold fusion

192

48 u

46

t

1

I

I

I

I

I

I

I

I

I

b.. 1 I

0.00 0.01 0.02 0.03 0.04 0.05 0.06

I2 Fig. 9. Reduced fissility parameter .( as a function of the squared asymmetry 1’. Because only the liquid-drop part of the fission barriers is interesting here, the data were corrected for the ground-state shell effects. They were calculated as differences of the liquid-drop masses of ref.22 ) and of experimental masses26). The solid line marked with “fit” is a quadratic approximation to the data. The full squares represent the data of this work. The other lines indicate the results of theoretical calculations: droplet, ref.50 ); liquid drop, ref.27 ); FRLD,

ref.44 ).

Pauli and Ledergerber 43) proposed to plot instead of the liquid-drop fission barriers Btd. the reduced fissionability parameter Z = Z’/(xA) [x - fissionability parameter from ref. *‘)I as a function of Z*. In the liquid-drop model *‘) the dependence 3 =f(Z*) is linear. When comparing the results of this work with the results of other measurements (fig. 9) it can be seen that the new data follow the trend of the older data. Also the recent predictions of the finite-range liquid-drop model of ref. 44) are not able to fit the data. The fission barriers for nearly all systems with small Z* values cannot be measured directly but only extracted by fitting measured cross sections with evaporation calculations. They can only be extracted in a model-dependent way ‘). If the energy or angular-momentum dependence of the level density has to be modified as was concluded in subsect. 5.2, also the value of the fission barrier fitting the data would be affected. In systems where the fission barrier B, is smaller than the neutron binding energy B,, the calculations are most. sensitive to the energy dependence of the level density and in systems with B, > B, the calculations are most sensitive to the angular-momentum dependence of the level density.

6. Fusion probabilities For all systems investigated here, fission is the dominant deexcitation channel at energies above the fusion barrier. Therefore it is difficult to discuss the whole fusion cross section when only the evaporation-residue cross section has been measured.

J.G. Keller et al. / Cold fusion

Total

fusion

cross sections

or, alternatively,

from the measured evaporation When fission is the dominant

193

fusion probabilities

cross sections, first. deexcitation process,

have to be derived

the evaporation-residue

cross

sections contain no information on the fusion of the high partial waves, because they will lead to fission. The surviving l-range (0 + 4Opt) corresponds to central collisions with impact parameters of less than 1 fm. Therefore we think it is more reasonable to derive fusion probabilities for central collisions from our data rather than total fusion

cross sections.

6.1. DETERMINATION

OF FUSION PROBABILITIES

Starting from the compound-nucleus model, the evaporation-residue can be written as a sum over all partial waves:

cross section

+ Q, 1))

(64

c,.,.(E)

= 7rh2c(21+

I)p(E,

+(E

I with p( E, 1) being the fusion probability at the center-of-mass energy E and the angular momentum 1, w( E + Q, I) the survival probability, and Q the reaction Q-value. In the conventional fusion model with one single fusion barrier, the fusion probability p( E, I) is equal to the transmission coefficient through this barrier. In the hypothetical case that all partial waves lead to fusion ( p( E, 1) = l), the evaporation cross section I$‘~,would be given by a0e.r. =7rX2~(2Z+l)w(E+Q,Z)_ In this expression the contributing angular-momentum which is determined by the angular-momentum-dependent The fusion probability averaged over the surviving given by the ratio of the measured evaporation-residue calculated

value

(6.2) range is limited by w( E, 1) fission competition. angular-momentum range is cross section u~,~,and the

I&

(P(E)),=L=

(E)

4,.(E)

77X2X(21 + l)p( E, f)w( E + Q, I) aX2C(2Z + l)w( E + Q, 1)

(6.3)

For calculating u&, the fission barriers were chosen to fit the measured cross sections u~.~,at the highest energies investigated here. Since the cross sections for evaporation of neutrons is reproduced much better by the evaporation code HIVAP than all other evaporation channels, in all cases, with the exception of 90Zr + 96Zr, the sum of all xn cross sections has been used for the evaluation of (p(E)),. For 90Zr + 96Zr the total evaporation-residue cross section was used. In order to facilitate the comparison of the measured fusion probabilities with theoretical predictions, it is desirable to determine the fusion probabilities for I = 0 from (p(E)),. Here this is a small correction justifying a simple approach.

194

J.G. Keller et al. / Cold fusion

The angular-momentum dependence of the fusion cross section can be described approximately by the increase of the fusion barrier due to the rotational energy: 4”#)

= %S(~ = 0) + E,,(Q)

J%tw

= p-(1+ h2 2#,,

l),

(64

where R,, is the location of the 1 = 0 barrier. Under this assumption the fusion probability for 1 = 0 can be calculated from (p(E)), as follows. The l-dependence of the fusion probability is connected with the energy dependence as ~(E,l)=p(E-E,,,1=0). The fusion probability

probability by

for p(E,

(6.5)

1= 0) can then be calculated

from the mean fusion

Pw=O)=(P(E+E,,)),. As an approximation for E,,, the averaged was calculated iteratively from

(Em,),=

(6.6) rotational

rX2Et21+&%,,(l)p(E, mh*C(21+

energy

l)w(E+

was taken.

Q, 1)

+(E+

l)p(E,

(Erot),

Q, 1)

67)

’

where p( E, 1) is calculated from eqs. (6.5) and (6.6) using the energy dependence (p(E)), as given by eq. (6.3): P(ET 1) =( p(E+ The survival

probabilities

(Em,),-

from (p(E)),

0.2 MeV to 1.2 MeV in center-of-mass

to p(E,

of

(6.8)

EKdl,>>,.

w( E + Q, 1) have been taken from the evaporation

described above. The result of the reduction

It

code as

1 = 0) is a small energy shift of

energy.

6.2. COMPARISON WITH MODEL PREDICTIONS

For made,

the theoretical

description

which are different

of subbarrier

fusion

with regard to the handling

several

attempts

of the dynamics

have been of the fusion

process. Let us first consider the data of the reaction 90Zr + 92Zr as an example to demonstrate the different model predictions. The simplest idea of fusion below the fusion barrier is the quantum-mechanical penetration of a one-dimensional barrier. This model is able to describe reactions like (Y+ HI + HI’ (HI - heavy ion). The fusion probability can be calculated with the WKB method. For heavy-ion reactions not too far below the barrier, the penetrability of the barrier can be also described by the Hill-Wheeler formula (6.9)

J. G.Keller et al. / Cold fusion

195

170 175 180 185 190 195 200

E,, Fig. 10. Comparison

(MeV)

of the measured data with a WKB calculation using the Bass potential calculations using gaussian barrier distributions.

and with two

with (6.10) where p is the effective mass. But already for systems like 0 + Sm [ref. 45)] and Ar + Sm [ref. &)] it was found that the fusion below the barrier can no longer be described by a one-dimensional barrier penetration. In accordance with these results it is impossible to describe our data by onedimensional

tunneling

(see fig. 10). The behaviour

of the fusion probability

around

the barrier is rather smooth. At fusion probabilities p -C 10-4, however, the increase of p with increasing energy is even steeper than predicted by a WKB calculation using the Bass potential 47). The phenomenon of enhanced fusion probabilities below the classical barrier was qualitatively explained by Esbensen4*). He argued that collective low-lying states influence the fusion threshold. If the period 7 = l/w, which is connected with the surface motion of these states, is longer than the timescale of fusion, the sharp fusion barrier will be replaced by a distribution of barriers. In a first approximation this leads to a gaussian distribution of barriers with a value of ur./Bfus = (4 + 2)% [refs. 46,48)], where uB is the standard deviation of the distribution. However, it turns out to be impossible to describe the data by using a gaussian barrier distribution, too. When a standard deviation u = O.O4B,, is used for the gaussian, the deviation is drastic. Even if the parameters of the gaussian are adjusted, the resulting description of the data is still rather poor (see fig. 10). The reason for the failure of this model is probably due to the fact that the excitation energies for the first excited states are rather high in this system.

196

J.G. Keller et al. / Cold fusion

The replacement of the sharp barrier by a gaussian distribution of barriers is correct only in the case that the amount of energy, necessary to excite the collective states, is neglected. In order to get a complete solution of the problem, a coupledchannels calculation has to be performed. In the last few years a model was developed which allows to solve the coupledchannels equations approximately. Calculations were performed for the Zr + Zr systems using the codes of ref. 49). The first 2+ and 3- states of projectile and target were taken into account, and the Bass potential was used. However, these calculations fail to describe the measured energy dependence as well as the differences between the systems (fig. 11). Apparently the coupling of the excited states to the fusion process is overestimated strongly. When taking into account more excited states - only known with sufficient accuracy for the nucleus 90Zr - the deviation between the data and the calculation even increases. In another approach developed by Cassing “) the behaviour of the single-particle levels was studied in a two-center shell model. The development of diabatic and adiabatic single-particle levels is studied as a function of the relative velocity. At energies far below the fusion barrier the region dominated by barrier penetration is shifted by a “shell effect” which depends on the nuclear structure of projectile and target. A fusion calculation based on this approach5’) is shown as a dotted curve in fig. 11 for the system 90Zr + 90Zr. For still heavier systems, for example Sn on various Zr isotopes, an additional dynamical hindrance of fusion is observed 6). If there is considerable density overlap at the fusion barrier, this so-called “extra push” has been predicted [refs. 5*51),and references therein]. Because of the very smooth behaviour of the fusion probabilities below the classical fusion barrier it is difficult to interpret the data in terms of an extra push. We will come back to this point in subsect. 6.3.3. Another attempt to explain the reduction of the fusion cross section in systems with considerable density overlap at the classical fusion barrier is the surface-friction model of Grosse, Friibrich and coworkers [ref. 52), and references therein]. However, up to now it has been difficult to calculate fusion cross sections below the average fusion barrier in the framework of this model.

6.3. DISCUSSION

To get an effective parametrization of the data we come back to a gaussian distribution of the fusion barriers. However, it is necessary to introduce a further parameter which describes the cut-off of the distribution on the low- and highenergy sides. The parameters are: (i) the mean fusion barrier Rdyn,or instead the difference Bdyn- BBassbetween the measured value and the model prediction from ref. 47),

J. G. Keller et al. / Cold@ion

197

100 10-l

s

lo+ 10-3

da

10-b

II_

10" 106 10-7 100 10-l

G

1o-2

&

10-3

ti a

lo-' 10-5 106 10-7

11.1

I

I

170

I

180

E,,

I

i

190

I

I

I

200

(MeV)

Fig. 11. Measured fusion probabilities as a function of center-of-mass energy. Arrows: fusion barriers calculated from the Bass potential. Dashed lines: Hill-Wheeler calculation shifted to describe the lowest energy data (adiabatic barrier). Do?ted line: calculation of C&sing 50) for v” Zr +90 Zr. Solid lines: calculation from ref.49 ) using the Bass potential. Dashed-dotted line: result of fitted barrier distribution (Cparameter fit). Additionally for them Zr +92 Zr the adiabatic barrier is marked by an arrow.

198

J. G. Keller et al. / Cold fusion TABLEI Parameters B Bass Reaction

90Zr +*9 Y 9OZr “Zr 90Zr wZr

+90 +92 +96 +94

Estimated

Zr Zr Zr MO errors

connected

to the fusion probabilities

%,,t

c

--

B dyn -

Brass

B adm

ha

-

Boas\

X,fl

[MeVI

B,,

+I”,1

WeVl

WcVl

x2

[McVl

0.702 0.714 0.710 0.701 0.733

177.2 181.7 180.9 179.4 189.9

2.4% 1.5% 2.3% 2.5% 2.5%

2.6 2.3 3.2 4.0 3.4

4.9 0.0 3.1 3.7 5.7

1.933 2.265 2.265 2.265 2.265

1.7 2.5 3.2 2.5 0.45

- 4.3 -4.4 -6.1 - 10.1 -7.2

of the fit parameters: AAw = 0.1 MeV,

A+,uct/cmxt

= 20% >

AC = 0.5~~~~~

(ii) the fluctuation width ufluct, (iii) the cut-off parameter c of the distributions, (iv) the ho of the potential barrier to describe the tunneling regime in the Hill-Wheeler approximation. This parametrization is already found in the literature *,18). However, for the present data this description is still not satisfying. This is indicated by the x2 of the fits which are too high (see table 7). Therefore we tried to analyse the data without a global parametrization for the fusion probabilities. 6.3.1. Barrier penetration. In the subbarrier region two regimes can be distinguished: While the slope d(ln(p))/dE is changing in the region near the conventional barrier, it becomes constant for fusion probabilities < 10e3 (see fig. 11). A constant slope is typical for a Hill-Wheeler-type barrier penetration. Therefore we think

that

the penetration

of the lowest barrier

is dominating

here. The

present data allow to study the penetration process over up to four orders of magnitude. For the first time in a heavy-ion fusion reaction the parameter fto of the fusion barrier (table 7) is measured to be considerably smaller than the value calculated from one-dimensional fusion models; the value for Aw for all the systems under consideration here is Aw = 3.2 MeV for the Bass potential 47), Aw = 4.2 MeV for the proximity potential 53), and Ro = 3.4 MeV for the Woods-Saxon potential used in ref. 49), when the reduced mass is taken as effective mass of the fusion barrier as is usually done. The data, however, may be described, when the effective ‘mass is increased by a factor of 2-4, dependent on the nuclear potential used. This is valid for the WKB as well as for the Hill-Wheeler approximation. A more accurate determination of the effective mass is not possible in view of the deviations between the fusion potentials. A similar effect is known from the spontaneous-fission halflives of the actinides, where effective masses considerably larger than the reduced mass of the fragments are needed 54). However, these values depend sensitively on the configuration during

J. G. Keller et al. / Cold fusion

199

10-69 10-7I 166

168

,/I 170

E,,

,,"' 172

17L

176

(MeV)

Fig. 12. Comparison of the fusion probability for the reactions 9o Zr + 90Zr (triangles) and 9o Zr + 89Y (squares). The three straight lines merging near 171 MeV have the slope of the “Y data (dotted line), of the 90Zr data (dashed line), and the slope from a WKB calculation using the Bass potential (solid line), respectively.

the penetration process which are different for fusion and for fission. Therefore a direct comparison is not possible. It is also for the first time that different values for Aw are found for neighbouring systems. This is demonstrated for the reactions 90Zr + 90Zr and 90Zr + “Y in fig. 12. The values for Aw of the other three even-even system (90Zr + 92,96Zr,94M~) investigated here are not in contradiction with the tie fitted to the data for the systems 90Zr + 90Zr. This leads to the conclusion that the observed difference may be caused by pairing effects. The influence of pairing on barrier penetration is well known from the spontaneous-fission halflives, too5’). It is thought to be connected with a level blocking due to the unpaired nucleon, and it is interesting to note that the same increase of about 15% in Aw per unpaired particle can account for the blocking effect in both processes, fusion and fission. 6.3.2. Lowest fusion barrier. With the help of the Hill-Wheeler tunneling following,

expression

for the

regime it is possible to extract the lowest barrier leading to fusion. In the this barrier will be called the “adiabatic barrier”. This name is incorrect

insofar as the lowest potential barrier separating the compound nucleus from two separated fragments is given by the fission barrier which is for 9o Zr +92 Zr = 10 MeV below the “adiabatic barrier”. But the time to search for the lowest barrier is limited by the barrier-penetration time. Therefore the so-called “adiabatic barrier” is the lowest barrier “felt” during the fusion process. As a measure for the adiabatic barrier we take the barrier Badia necessary to describe the asymptotic trend of the data by the Hill-Wheeler formula. When comparing the asymptotic shift, defined as the difference BBass - Badia of the fusion barrier as predicted by the Bass potential and the adiabatic barrier, for

200

J. G. K&r

et al. / Cold fusion

“‘MO

‘O”Ru -P 3

‘O*Ru 6-

48

50

52

Neutron

54

56

number

58

60

62

of target

Fig. 13. The asymptotic shift BBass - Badia as a function of the neutron number in the target nucleus. The filled circles are the data of this work with %Zr projectiles; the open circles are results obtained with X6Kr projectiles ‘,‘s).

the different systems investigated here (see table 7) a correlation between the neutron number in the target and the asymptotic shift can be observed (fig. 13). Within the errors the asymptotic shift is the same for 90Zr and 89Y and 94Mo, respectively. This shows the strong connection between asymptotic shift and the nuclear structure which is dominated by the N = 50 shell for the nuclides around zirconium. The data of Reisdorf et al. *) also show the nuclear structure effect of the N = 50 shell, although much weaker, see fig. 13. One reason for this may be that 90Zr used here as projectile is more stiff than 86Kr which was used in ref. *), as can be seen from the energies of the first excited levels. Also an important role. Both effects may lead to structure of the target isotope in the case of the 6.3.3. Barrier distributions. In order to avoid

nucleon transfer reactions may play a higher sensitivity on the nuclear 90Zr projectile. a fixed parametrization we tried to

unfold the data to obtain the fusion-barrier distributions. From ref. 49) the connection between the fusion probability distribution

f( B,,)

p(E)

and the barrier

is given by P(E)

=Jf(%&(K

Brus)d&,,

(6.11)

where the transmission coefficients T( E, B,) may be expressed in the Hill-Wheeler approximation by eq. (6.9) By use of an unfolding procedure56,57) the barrier distributions could be extracted. For Aw we used the values determined in the tunneling regime (see table 7). The resulting barrier distributions as reproduced in fig. 14 are well defined on the low-energy side. On the high-energy side the result of the unfolding procedure is

100 _~ 10-l

&

1o-2

rc 10-3 lo-” 10-5 loo _uI 10-l &

10”

+

lo+ lo-” 1o-5 100

_* 10-l $$ 10-Z Y- 10-3 lo-& to-5 loo _~ 10-l 6

1o-2

y-

10-a lo-’ 10-5 100

_~ 10-l &

10-2

rc

1o-3 1o-L 10-5

170 180 190

200

210

E (MEW Fig. 14. Barrier distributions for the systems under consideration. Histograms: results of the unfolding procedure; dashed orea: errors from the unfolding procedure; pointed area: continuation of the histogram into the region where the error bars are larger than the values. Dashed-dotted line: result of the 4-parameter fit. Vertical bars: eigenvalues with their corresponding weights from ref.49) taking into account the first 2+ and 3- states of projectile and target, normalized to a width of 1 MeV; eigenvalues within 500 keV have been lumped together.

202

restricted

J. G. Keller et al. / Cold fusion

by the normalization

condition

j-m”,)d%, = 1. When comparing above, significant

(6.12)

the results with the parameterization of a cut-off gaussian as used deviations are found. There are peaks in the barrier distribution

which partly seem to be correlated to eigenvalues of the coupled-channels calculation49). However, the weights of the low-energy eigenvalues seem to be strongly overestimated by this model. The barrier distribution (B,,) found for 90Zr + 90Zr is much narrower than that for all other systems. One single proton less (90Zr + *‘Y) broadens f( Br,,) by nearly a factor of two, although the asymptotic barrier shift (BBass - Badi,) remains almost constant. These strong structural effects found in the barrier distributions tend to rule out a strong influence of the “extra-push” phenomenon in these systems which is related to liquid-drop properties. Moreover, table 7 shows that there is no correlation between Bdyn - BBass and x,rr, the scaling parameter of the extra push.

7. Conclusion In the present experiments the process of the deexcitation of nucleus only by y-radiation after fusion of two partners, both having larger than 20, was observed for the first time. It was shown that energy at the fusion barrier is essential for the understanding of cold When

184Pb instead

for radiative competition.

of 18’Hg is formed

as a compound

nucleus,

the compound mass numbers the excitation fusion.

the cross section

capture is decreasing by a factor of 25 because of the increasing fission For even heavier systems, the extra-push phenomenon was found to

increase the fusion barrier considerably 6). It is expected from the Q-value systematics that for systems lighter than those under consideration the excitation energy at the fusion barrier is growing, too. Therefore the cross sections for radiative capture of the systems investigated here are probably the highest obtainable in heavy-ion reactions. For a given compound nucleus the cross sections for all xn channels as well as for the radiative capture channel can be well reproduced in the framework of the statistical model assuming the same El strength for all channels. A strong dependence of the fusion probabilities on the nuclear structure in the entrance channel was found. The differences between the systems under consideration cannot be described by recent fusion models. It is not possible to reproduce the data with the coupled-channels model of ref. 49) which takes into account the influence of collective excitations on the fusion process, while the fusion cross sections for Ar + Sn and Ar + Sm”) could be reproduced.

Evaporation-residue corresponding

to fusion

cross

J. G. Keller

et al.

sections

are measured

probabilities

/ Cold fwion

of p(E)

203

betwen

-c 10p6.

50 mb

The fact that

and

10 nb,

the energy

dependence in the region p < lop4 is steeper than predicted by the WKB method using one-dimensional fusion models, possibly indicates that the effective mass necessary in the penetration calculation is considerably larger than the reduced mass. There are also indications for pairing effects on the penetration process from the different Aw values fitted for the reactions 90Zr +90Zr and 89Y. Both effects, which are well known from the spontaneous-fission halflives of actinides are observed here for the first time in heavy-ion fusion process. A method was developed to deduce fusion barrier distributions from measured fusion probabilities. We thank P. Armbruster for his encouraging interest in this work, and W. Cassing for many fruitful discussions. We are especially indebted to H. Stelzer for the preparation of the position-sensitive support of the Bundesministerium

parallel-plate fur Forschung

avalanche counter. Financial und Technologie is gratefully

acknowledged. References 1) Proc. Int. Conf. on fusion reactions 2) 3) 4) 5) 6) 7) 8)

9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

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