Nuclear Instruments and Methods in Physics Research B 93 (1994) 103-106 North-Holland

NUMB Beam Intemctlons

with Materials 8 Atoms

Letter to the Editor

On ionic charge distributions of heavy evaporation residues passing through a carbon foil

R.N. Sagaidak * and A.V. Yeremin Flerou Laboratory of Nuclear Reactions, JINR, Dubna 141980, Russian Federation

Received 29 October 1993 and in revised form 21 January 1994

Parameters of the ionic charge distributions, i.e., mean charge values and charge distribution widths for very heavy (2 2 53) ions passing through a carbon foil were analyzed from the view point of applicabiii~ of known empirical systematics. Strong deviations (up to 60%) for ex~rimental mean charge values were obtained from those deduced from empirical formulae at ion energies of < 0.1 MeVfamu. Corrections providing a general agreement with the experimental data within + 6% at the ion energies of 0.001 I E 5 10 MeV/amu to the formufa of Shima et al. are proposed. New systematics of the widths of charge distributions are also presented. The obtained systematics were used in ion-optical calculations of transportation of evaporation residues through the electrostatic recoil separator VASSILISSA.

Knowledge of the ionic charge distributions (ICD) for heavy ion reaction products, especially for the heavy evaporation residues (ER), is important from the point of view of effective work of the kinematic recoil separators, i.e., achievement of optimum transmission (see e.g. the recent review ref. [l] and refs. therein). The ICD of the ER formed in a nuclear reaction and knocked out from a target is not an equilibrated one. A possible transfer of nuclear excitation to the inner atomic shells and subsequent de-excitation of moving atoms via a cascade of Auger electrons make the ICD of ER unpredictable. A carbon foil placed at a position of several centimeters downstream from the target restores the equilibrium of the ICD of ER [2].

Applications of the empirical systematics for the equilibrated ICD [3,4] in ion-optical calculations for the case of specific separation systems [5,6] showed significant deviations of the calculated transportation efficiencies for the ER from the experimental ones 17-91. Evidently, this is caused by differences of the adopted ICD from the real ones. Indeed, the data on the ICD for the heavy ER are poor [Z]. Therefore the empirical systematics of mean charges (4) and charge distribution width d [3,4] based on the data obtained for lighter (Z 5 36, mostly at E 2 1 MeV/amu) heavy ions passing through a carbon foil are used for ion- optical calculations. We considered the available ex-

* Corresponding author, c/o Prof. M.G. Ithis, tel. +7 095 Fig. 1. Experimental mean ionic charges (q&r/Z vs re- 924 3914, fax +7 09.5 97.5 2381, e-mail oyuts@ljar.jinr. duced ion velocity X (see text). The empirical curve of Shima

dubna.su. et al. [4] (q)s~~ /Z vs X (Eq. (1)) is also shown.

perimental data on ICD for Z z 53 heavy ion beams at nonrelativistic energies (E I 10 MeV/amu) compiled in refs. [lo-121 (see also refs. therein1 and the recently obtained data [13] along with the data for ER [Z]. The comparison of these data for mean charges (rl)exp/Z with the predictions given by the empirical formula of Shima et al. [4] is shown in Fig. 1 as a function of reduced velocity X [3]. The mean charge is expressed in this formula as

(q)SIM/Z = 1 - exp( - 1.25X+ 0.32X2 - 0.11X3),

X= 3.86fi/Z”.45, (I)

s Ta

lo- $0 Y

\ -

1 o-2 1 O-l 100 X

0168-583X/94/$07.~ 0 1994 - Elsevier Science B.V. Ah rights reserved SSDI 0168-583X(94)00150-T

104 R.N. Sagaidak, A. K Yeremin /Nucl. Instr. and Meth. in Phys. Res. B 93 (1994) 103-106

1 .2 I 1 Table 2

i

- - polynom.

+lO% - deformres.

100 E (MeV/amu)

Fig. 2. (q&,/(q)SIM vs ion energy E (0.1 < E < 10 MeV/ amu). The results of a least-squares fit are shown: solid line

Eq. (2), dashed line polynomial (for comparison).

where Z is the ion atomic number and E is the ion energy in MeV/amu.

The strong deviations of the experimental data from the predictions (up to 40%) and bad scaling with Z in the energy range of our interest 0.01 < E < 0.1 MeV/amu (X< 0.2) are seen from Fig. 1. This is observed for both systematics [3,4]. Considering the other ones, similar discrepancies were observed [14]. A close comparison of the experimental data with the predictions of Eq. (1) at the energies E > 0.1 MeV/amu gives a minor, but systematic, “resonant- like” dependence of the (q)exp/(q)SIM values versus E, as it is shown in Fig. 2. A similar dependence is observed when the same values are plotted against X. These deviations are within a range of about +_lO% and they are invisible in the log-log plot of reduced values used in Fig. 1.

An improvement of the empirical systematics of ICD [3,4] in their application to the very heavy ions is the goal of this study. To improve the ( q)SIM systemat- its we considered the ratio R(Z, E) = (q),&(q)SIM.

Table 1 Fitted constants in Eqs. (2) and (3)-(6) of the correction function (7) to the mean charge evaluation given by Shima et

al. [41 (Eq. (1))

f,(E) f,(E, Z) . p, = 0.95001 pz = 0.01488 ps = 0.35744 pq = 0.30325 ps = 2.78276

._ a, = 1.088 az = 5.990 X 10” b, = 5.158~ 1O-2 b, = 3.254 x 10” (Y = 16.993 /3 = 29.353

Spline interpolated parameters a(Z) and b(Z) in Eq. (3). Linear extrapolation is used for Z > 92

Z

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108

a(Z)

1.0000

b(Z)

0.0000 1.0156 9.640~ 1O-3 1.0308 1.909x 10-2 1.0455 2.814x 1O-2 1.0592 3.661 x 1O-2 1.0718 4.430 x 10-2 1.0829 5.101 x 10-2 1.0921 5.653x 1O-2 1.0989 6.052x 1O-2 1.1025 6.264X lo-* 1.1024 6.253 x lo-* 1.0979 5.984 x 10-a 1.0888 5.456~ 1O-2 1.0776 4.803 x 10-a 1.0671 4.193 x 10-2 1.0603 3.795 x 10-a 1.0599 3.777x 10-r 1.0691 4.308X 10-r 1.0906 5.554x 10-a 1.1260 7.596~ 10W2 1.1716 0.1015 1.2223 0.1286 1.2729 0.1547 1.3178 0.1773 1.3518 0.1940 1.3695 0.2025 1.3656 0.2003 1.3346 0.1850 1.2892 0.1628 1.2847 0.1605 1.2889 0.1625 1.2899 0.1629 1.2881 0.1619 1.2839 0.1598 1.2775 0.1566 1.2693 0.1525 1.2597 0.1477 1.2491 0.1424 1.2377 0.1368 1.2260 0.1310 1.2142 0.1251 1.2025 0.1193 1.1907 0.1134 1.1789 0.1076 1.1672 0.1017 1.1554 9.591 x 10-2 1.1436 9.006x 1O-2 1.1318 8.422x 1O-2 1.1201 7.838 x 10m2 1.1083 7.254~10-~ 1.0965 6.670x 1O-2 1.0848 6.085 x 1O-2 1.0730 5.501 x 1o-2 1.0612 4.917x 10-2 1.0495 4.333 x 1o-2 1.0377 3.749x 1o-2

R.N. Sagaidok, A. K Yeremin /Nucl. Instr. and Meth. in Phys. Res. B 93 (1994) 103-106 105

Table 2 (continued)

z n(Z) b(Z)

109 1.0259 3.165x lo-’ 110 1.0141 2.580 x 10-Z

For E 2 0.1 MeV/amu R(Z, E) =_f,(E), which was approximated by a deformed resonant function:

~~(E)=p,+(pzT/[(E-P?)2+,2]},

r=~sfI - exp( -p&)1, (2)

as it is shown in Fig. 2. The values of the constants pi-p5 were obtained from least-squares fitting to the data at the energies 0.1 zz E I 10 MeV/amu (see Table 1). It should be remarked that the use of the deformed resonant function is merely the best way to reach a better agreement of the values given by empirical for- mulae, i.e., Eqs. (1) and (21, and the experimental data at the high energy region (0.2 IX I 2). We cannot propose any “physical meaning” for the use of Eq. (2) now. The next point should also be taken into consid- eration. The accepted Z-scaling seems to be fulfilled only approximately within the notion of Eq. (1). The (q) values will be siightly underestimated (within 6%) for the group of “lighter” (I-Nd) ions and the same values will be slightly overestimated (within 6%) for the group of “heavier” (Ta-U) ions.

For E s 0.1 MeV/amu we chose for RG, El = f&Z, El the form:

f2(Z* E) = a(Z)E~(Z). (3)

To find the parameters a(Z) and b(Z) we derived the values az and 6, by fitting Eq. (3) to the available data at low energies for different Z. The obtained az, 6, values have been fitted to a function of the form

u(Z) = a, + @*f(Z), (4)

6(Z) = 6, +62f(r), (5)

f(z) = z* exp( -@), 2 = (Z - 53)/53. (6)

The constants ai, u2, 6,, b,, cy and p determined from the fit are listed in Table 1. To consider the detailed behavior of a(2) and b(Z) a spline interpolation com- bined with a linear extrapolation for Z > 92 was made. The obtained coefficients a(Z) and b(Z) are listed in Table 2. The fit of the parameters of Eq. (3) was satisfying the condition of matching with the function (2) at E = 0.21 MeV/amu, where the approximate equality f,(E) =f&E, Z) = 1 was fulfilled.

Combining Eqs. (2) and (3) the correction function to the formula of Shima et al. fir] could be expressed as

R(K 2) =kf,(E) + (I- k)fAK Z),

where k = 1, E ;r 0.21 0, E <0.21 (7)

3 1.2 I I” “* “,,“‘I “““8 “’ Q 0 0 b)

- - - - - -h-A- - 0.8 ’

1 o-3 1 o-2 1 o-1 100 101 E (MeV/amu)

Fig. 3. The same as in Fig. 2 except for the application of the correction function of Eqs. (Z)-(7) and energy region (0.001 < E < 10 MeV/amu). Low energy corrections are given with the parameters a(Z) and b(z) of Eq. (3) obtained from (a> a least-squares fit using Eqs. (4)-(6) with the constants in Table 1, and (b) sphne interpolation with the parameters in Table 2.

Fig. 3 illustrates the data of Fig. 1 corrected with Eqs. (2)-(7). A general agreement is achieved for the whole energy range. This agreement is within rt 6% for the spline interpolated a(Z) and b(Z) (Fig. 3b) and slightly worse for these parameters determined by the least-squares appro~mation (Fig. 3a) at low energies.

1.01 “” 1

0.8

5 0.6

Cl

; 0.4

0.2

o.o* 1 o-2 1 o-1 100

<q>exp I z

Fig. 4. Systematics of the charge distribution width (symbols are the same as in Fig. 1). The solid line is the result of a

least-squares fit using Eq. (8) with constants in the text.

106 R.N. Sagaidak, A.K Yeremin /Nucl. In&. and Meth. in Phys. Res. B 93 (1994) 103-106

30 '92Pb-ER a>

-10 15 20 25 Charge state (q)

Fig. 5. Some examples of the ionic charge djstribution. Experi- mental data [2,16f are shown as filled circles, our predictions using Eqs. (l)-(8) are shown with solid lines, calculations by Nikolaev and Dmitriev [3] are shown with dotted lines and calculations by Shima et al. [4,15] are shown with dashed

lines.

We obtained atso a new systematics of the charge distribution width. Fig. 4 displays the y = d,@.” vai- ues [15] plotted against x = (y&,/Z for the available data for 2 2 53. We fitted a function of the form

y =RuB exp(-Cx) @1 to the data, by the least-squares method. The best values obtained for the fitting constants were

A = 2.10176, B = 0.510987, and C = 1.68505. The presented systematics of the mean charges and

the charge distribution widths were used to predict ICD for some heavy ions and ER. The predicted distributions are shown in Fig. 5 along with similar ones obtained from the other predictions {3,4,15] and some experimental distributions for ER [2] and U ions [161 passing through a carbon foil.

Our estimations of the ICD are used for the com- puter simulation of the ER transportation through the electrostatic recoil separator VASSILISSA [6]. A good agreement was achieved between the calculated and experimental transportation efficiencies for the PO-AC ER in the investigated energy region of IO-40 MeV 1171. Carrying out the experiments on synthesis of 258105 in the reaction 27Alf236U,Sn) [IS], the shown ICD for

the 258105 (Fig. 5~) was used for the optim~2ation of the separator parameters.

The authors would like to thank Prof. G.M. Ter- Akopian for his encouragement and suggestions in editing the manuscript.

References

ill

L!l

[31

141

151

f61

01

181

M

DOI Ill1

I121

1131

[I41

D.51

1161

El71

081

G. Miinzenberg, in: Handbook of Nuclear Decay Meth- ods, eds. W. Greiner and D.N. Poenaru (CRC Press) in press; 69-92-76 (1992). N.K. Skobelev, V.Z. Maidikov and N.T. Surovits~ya, Z. Phys. A 314 (1983) 5. V.S. Nikolaev and 1-S. Dmitriev, Phys. Lett. A 28 (1968) 217. K. Shima, T. Ishihara and T. Mikumo, Nucl. Instr. and Meth. 200 (1982) 60.5. G. Miinzenberg, W. Faust, S. Hofmann, P. Armbruster, K. Giittner and H. Ewald, Nucl. Ins&. and Meth. 161 (19799) 65. A.V. Yeremin, A.N. Andreyev, D.D. Bogdanov, V.I. Chepigin, V.A. Gorshkov, A.I. Ivanenko, A.P. Kabachenko, L.A. Rubinskaya, EM. Smirnova, S.V. Stepantsov, E.N. Voronkov and G.M. Ter-Akopian, Nud. Instr. and Meth. A 274 (1989) 528. W. Faust, G. Miinzenberg, S. Hofmann, W. Reisdorf, K-H. Schmidt, P. Armbruster and K. Giittner. Nucl. Ins&. and Meth. 166 (1979) 397. H.W. Gggeler et al., Proc. Int. School Seminar on Heavy Ion Physics, Dubna, 1989 (JINR D7-90-142, 19901 p. 119. A.V. Yeremin, A.N. Andreyev, D.D. Bogdanov, A.P. Kabachenko, O.N. Malyshev, O.A. Urlova, GM. Ter- Akopian and V.I. Chepigin, JINR E15-90-347 fDubna, 19901. A.B. Wittkower and H.D. Betz, At. Data 5 (1973) 113. K. Shima, T. Mikumo and H. Tawara, At. Data Nucl. Data Tables 34 (1986) 357. K. Shima, N. Kuno, M. Yamanoucbi and H. Tawara, At. Data Nucl. Data Tables 51 (1992) 173. E. Baron, M. Bajard and Ch. Ricaud, Nucl. Instr. and Meth. A 328 (1993) 177. A.G. Popeko, R.N. Sagaidak and A.V. Yeremin, Proc. Int. School Seminar on Heavy Ion Physics, Dubna, 1993 (JINR E7-93-274, vol. II) p. 511. K. Shima, N. Kuno and M. Yamanoucbi, Phys. Rev. A 40 (1989) 3557. A.B. Wittkower and H.D. Betz, Phys. Rev. A 7 (1973) 159. A.V. Yeremin et al., Proc. Int. School Seminar on Heavy Ion Physics, Dubna, 1993 (JINR E7-93-274, vol. I) p. 109. A.N. Andreyev et al., 2. Phys. A 344 (1992) 225.