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Charge exchange processes for semi-relativistic helium ions (β = 0.51) in solid gold
Nuclear Instruments and Methods in Physics Research B 235 (2005) 368–373 www.elsevier.com/locate/nimb
Charge exchange processes for semi-relativistic helium ions (b = 0.51) in solid gold A. Go´jska a,*, D. Chmielewska a, J. Rzadkiewicz a, Z. Sujkowski a, T. Adachi b, H. Fujita b, Y. Fujita b, K. Hara b, Y. Haruyama b, J. Kamiya b, H. Ogawa b, M. Saito b, Y. Shimizu b, Y. Shimbara b, M. Tanaka b, H.P. Yoshida b, I. Katayama c The Andrzej Soltan Institute for Nuclear Studies, 05-400 Otwock–S´wierk, Poland b RCNP and Department of Physics, Osaka University, Japan IPNS (Institute of Particle and Nuclear Studies), KEK (High Energy Accelerator Research Organization) Oho 1, Tsukuba, Ibaraki 305-0801, Japan a
c
Available online 13 May 2005
Abstract Interactions of 150 MeV/amu 3He++ projectiles with solid gold targets have been studied at the isochronous cyclotron of the RCNP in Osaka. The 3He+ ions resulting from capture of the target electrons to the projectile were observed with the use of large magnetic spectrograph, Grand Raiden, set at h = 0 with respect to the beam. The yield ratio of singly to doubly ionized helium ions emerging from thin gold foils, He+/He++, has been measured as a function of the foil thickness. Extrapolating the results to zero Au target thickness permits to determine the cross section values for electron stripping from 3He+ ions, rSTRIP = 1.05 · 1017 cm2, and for electron capture to 3He++ ions, rCAP = 1.12 · 1025 cm2. The results obtained extend significantly the existing systematics for both processes to high (semi-relativistic) velocities. The collision strength deduced from the stripping cross sections deviates strongly from the theoretical predictions of Gillespie in absolute values as well as in the velocity dependence. It can, however, be well approximated by the simple Bohr formula for mid Z atoms. Also the capture data indicate the need to improve the theoretical approximations. A more detailed treatment of electrons captured from different shells in a high Z target is presumably needed. The astrophysical interest in the data of this kind for very light ions (hydrogen, helium) is indicated. 2005 Elsevier B.V. All rights reserved. PACS: 34.50.Fa; 34.70.+e Keywords: Charge exchange; Ionization (stripping); Capture
*
Corresponding author. Fax: +4822 779 34 81. E-mail address: [email protected] (A. Go´jska).
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.03.207
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
1. Introduction The dominant processes occurring to a fast ion traversing a solid are the capture of electrons from the target atoms to the vacant states in the ion and the stripping of the bound electrons from the ions. These charge exchange processes are of primary interest for understanding the passage of ions through matter. Though known and studied since the early days of atomic and sub-atomic physics, they are still only crudely described theoretically. The experimental information is also limited, particularly for light projectiles at intermediate and high (relativistic) energies. Because of huge differences in cross-sections between the capture and the stripping processes the experiments require very special techniques of advanced nuclear physics. The capture of electrons by an ion colliding with an atom proceeds via two processes: the Radiative Recombination, RR, and the NonRadiative Electron Capture, NREC. To the extent that the captured electron can be considered as free and at rest, the RR process corresponds to the Radiative Electron Capture, REC, which is the time reversed photo-electric effect on the partly ionized projectile atom. The NREC process cannot occur for free electrons. The momentum and energy conservation conditions require the presence of a third body, in this case the atomic nucleus of the target atom. The cross section, rNREC, depends sharply on the energy of the ion, EP, and on the atomic number of the target, ZT, as well as of the ion, ZP. It has a maximum close to the velocity matching condition, vp ve, where vp and ve are the velocities of the ion and the captured electron, respectively. For vp ve rNREC Z 5P Z 5T E6 P .
ð1Þ
Due to sharp ZT dependence the NREC process dominates for high Z targets and the total capture cross section, rCAP rNREC. In contrast, the ionization cross section, rSTRIP, depends smoothly on EP and Z. Crudely, rSTRIP
Z 2T 1 E . Z 2P P
ð2Þ
369
A review of the various processes occurring in the relativistic ion – atom collisions is given in [1] (see also [2] are Refs. therein). Recent experimental information on interaction of fast helium ions with various gaseous and solid targets can be found in the work of Katayama et al. [3–5]. These authors have measured the stripping and the capture cross section for 3He ions with energies up to 43.4 MeV/amu. The present work extends this information to much higher 3 He energy, 150 MeV/amu, for Z = 79. The results are compared with basic theories. Interaction of relativistic helium ions with atoms as well as with free electrons is of primary astrophysical interest [2]. Likewise, information on the charge exchange process involving fast ions is much needed in hot plasma diagnostics.
2. Theoretical predictions Collisions between fast ions and target atoms lead to electron capture to the vacant states in the ions. The impinging ions may also lose electrons in the ionization process, i.e. in the stripping of the bound electrons from the ion to the continuum. The ionization (stripping) process is described by Bohr [6] and Gillespie [7,8]. The electron capture cross section is given by the approximate calculations according to Oppenheimer–Brinkmann–Kramer [9–11] OBK, and Nikolaev [12,13] calculations. More realistic expressions in the relativistic eikonal approximation are given by Eichler [1,14]. The first description of electron ionization process was given by Bohr [6]. Three approximate expressions for the electron stripping were given for high, low and medium Z of target, correspondingly. The expression for high Z takes the particularly simple form rSTRIP ðhigh ZÞ pa20 .
ð3Þ
The Bohr predictions for mid Z targets include the screening effects due to tightly bound inner electrons 2=3 Z v0 rSTRIP ðmid ZÞ ¼ pa20 T ; ð3aÞ ZP v
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
370
where the Bohr radius a0 = 5.29 · 109 cm, the Bohr velocity v0 = 2,19 · 108 cm/s, v is the ion velocity, ZT is the atomic number of target and ZP is the atomic number of the projectile. The electron stripping cross section can be described by an asymptotic (high-speed) expansion form of the Born approximation. According to Gillespie [7,8] v 2 0 rSTRIP ¼ 8pa20 I ; ð4Þ v where the parameter I called the ionization collision strength is given by an integral over the momentum transfer 1.24 I 2 Z T ð1 þ 0.105Z T 5.4 104 Z 2T Þ. ð5Þ ZP A simple description of the NREC cross section is given by the OBK (Oppenheimer–Brinkmann– Kramer) theory which neglects the internuclear interaction in the perturbing potential. Only the interaction between the target electron and the incident ion is taken into account [1]. The cross section is expressed by the asymptotic equation 18 12 22 5 5 v0 rOBK Z ¼ pa Z . ð6Þ CAP 0 5 P T v The electron capture is a three body problem. The interaction between incident and target nuclei has to be taken into account. The electron capture cross section values calculated in the first order OBK approximation Eqs. (6) and (7) are larger than the experimental ones. The calculation in the second order B2 approximation [1]: v 5p 1 0 OBK rB2 ¼ r 0.295 þ ð7Þ CAP 211 Z P þ Z T v gives somewhat lower but still overestimated cross section values. A method to overcome these difficulties, proposed by Nikolaev [12], [13], included arbitrary external and internal screening corrections for the electron capture cross section from inner shells of the target to the vacant state in the ion 5 29 p n1 n2 2 v1s NIK rCAP ¼ n10 ðhÞ 5 v v2s
U4 ½ð1 hÞn2 ðhÞ ½1 þ ð1 hÞn2 ðhÞ
3
;
ð8Þ
where n1, n2 are quantum numbers of projectile and the target states, respectively, v1s = v0Z1/n1 and v2s = v0Z2eff/n2 are the orbital velocities of electron in the projectile and in the target, respectively, and v2s ffi; nðhÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð9Þ 2 v1s þ q2 ðhÞ Eb
with h ¼ Eii , Ebi is a binding energy taken from tables [15], Ei ¼ R Zneff2 .
Here qðhÞ ¼ 12 v þ v22s h v21s =v is the minimum momentum transfer.
3. Experiment Thin gold targets were bombarded with 150 MeV/amu 3He++ ions extracted from the ring cyclotron of the RCNP Osaka. The intensity ratio of singly to doubly ionized He ions leaving the target, R = Y(He+)/Y(He++), was measured as a function of the target thickness. In view of the rSTRIP value being about 108 times larger than rCAP this ratio is strongly thickness dependent. The yield of He+ ions corresponds to the survival probability of an ion which has captured an electron and escaped from the target prior to the subsequent electron stripping. At saturation, i.e. for x ! 1, R = rCAP/rSTRIP [16]. By fitting the function R = a[1exp(bx)] to the measured R(x) values we can obtain separately the relevant cross sections. Here a = rCAP/rSTRIP and b = rSTRIP. Singly ionized 3He+ ions together with tritons from the (3He, t) reaction were detected in the focal plane of the magnetic spectrometer Grand Raiden [17] set at h = 0 with respect to the beam, with vertical and horizontal angles of 40 mrad each. The 3He++ beam was fully intercepted by a Faraday cup placed in the first dipole magnet of the spectrometer. The set-up was identical to that used routinely by the Osaka group to study the Gamov–Teller strength distribution in the (3He, t) charge exchange reactions see e.g. [18]. Thin gold targets were prepared by evaporating gold onto 5 lg/cm2 thick carbon foils. The thicknesses of gold layers were measured in a separate scattering chamber with 5–10% accuracy. Targets 5.5, 9.6, 22.7 and 133.25 lg/cm2 thick were used.
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
The thick Au target of 1700 lg/cm2 was obtained commercially.
4. Results and discussion The measured yield ratio of the Y(3He+)/ Y( He++) versus the target thickness is presented in Fig. 1. The fitted cross section values are rSTRIP = (1.05 ± 0.19) · 1017 cm2 and rCAP = (1.12 ± 0.27) · 1025 cm2. The errors do not include uncertainties due to the possible surface contamination of the targets with light elements (carbon, oxygen). Approximate corrections for this effect lower the yield ratio values and introduce asymmetric errors to the final results. In order to reduce these errors the experiment was repeated several times for each target. The self– 3
Y( 3 He+ )/Y( 3 He ++)
150 MeV/amu 3He->Au 1.2x10
-8
8.0x10
-9
4.0x10
-9
0.0 10
100
1000 2
target thickness (µg/cm )
Fig. 1. The Y(3He+)/Y(3He++) yields as a function of target thickness for Au target. Points represent an experimental data. The curve show the results of fitting with Eq. (1).
cleansing effect of the beam on the target due to the sputtering of light impurities was sometimes observed. Only the ‘‘post-cleansing’’ data were included in the analysis. We attribute an additional 10% uncertainty to the final values to take the impurity effect into account. The existing data on the stripping cross section in the energy range 17.3–43.3 MeV/amu, supplemented by the present value at 150 MeV/amu, are collected in Table 1 and in Fig. 2. The theoretical values calculated according to formulae (3), (3a) and (4) are included for comparison. Table 2 presents essentially the same information in terms of the collision strength. This is illustrated in Fig. 3. It is seen that the Bohr (high Z) and the Gillespie approximations grossly overestimate the cross section values, while BohrÕs mid Z formula reproduces the data. This might indicate the importance of the screening effect even for the heavy, Z = 79, atom. The data for total capture cross sections for He interacting with gold are collected in Table 3 and illustrated with Fig. 4. A comparison of the data with the OBK, B2 and Nikolaev – type calculations shows that the first two overestimate the effect dramatically. Calculations according to Nikolaev reproduce the experiment at b = 0.51 (the present result) and deviate from the data at lower velocities up to about a factor four. Calculations following the eikonal approximation of Eichler [1] remain to be done before drawing detailed conclusions from this result. The present work is a part of a larger programme of studying charge exchange processes for high speed very light projectiles interacting
Table 1 The experimental and theoretical values of the ionization cross section of 3He+ interacting with Energy (MeV/amu)
b = v/c
17.3 20.5 24 33.1 43.4 150
0.19 0.21 0.23 0.26 0.29 0.51
79Au
at various projectile velocities
Stripping cross section * 1017 cm2 Experimental
3.51 2.96 2.93 2.37 1.66 1.05
(42) (35) (35) (28) (20) (19)
371
Ref.
Theoretical Bohr low Z
Bohr mid Z
Gillespie
79.7 67.4 57.8 43.8 34.4 11.5
3.06 2.82 2.61 2.27 2.01 1.17
14.6 12.4 10.6 8.04 6.32 2.12
[5] [5] [5] [3] [3] Present results
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
372
Fig. 2. The experimental (points) and calculated electron stripping cross section. The solid line is from calculations of Gillespie formula. The other are from Bohr approximation: dash line is for high Z, dotted line for mid Z and dash-dot is for low Z targets.
Fig. 3. Measured and calculated collision strength for 3 He ! Au at various projectile velocities. Solid line represents calculations using Bohr approximation for intermediate Z. The dotted line shows collision strength from Gillespie cross section.
Table 2 The experimental and theoretical values of the ionization cross section in terms of collision strength Energy (MeV/amu)
b = v/c Collision strength
Ref.
Experimental Theoretical Bohr Gillespie mid Z
17.3 20.5 24 33.1 43.4 150
0.19 0.21 0.23 0.26 0.29 0.51
34.76 34.70 40.12 42.81 38.3 71.95
30.37 33.02 34.15 40.98 46.24 79.87
147 147 147 147 147 147
[5] [5] [5] [3] [3] Present results
Fig. 4. The experimental (points) and calculated electron capture cross section. The solid line is from Nikolaev formula, dash line is from OBK and dotted line from B2 approximations.
with various targets (ranging from Z = 4 up to the heaviest targets available). Preliminary results for REC, NREC and stripping processes for Z = 6
target have been presented in [19]. Data for targets 6 < Z < 79 are being processed.
Table 3 The experimental and theoretical (OBK, B2 and Nikolaev) values of electron capture cross sections for 3He++ ! 79Au Energy (MeV/amu)
b = v/c
Electron capture cross section 1022 cm2 Experimental
22.6 33.1 43.4 150
0.22 0.26 0.29 0.51
1.41 (14) 0.413 (41) 0.202 (24) 0.00112 (27)
Ref.
Theoretical OBK
B2
Nikolaev
9710 1090 256 0.363
2860 321 75.5 0.107
0.374 0.125 0.0605 0.0010
[4] [4] [3] Present results
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
Acknowledgements We acknowledge with pleasure the excellent working conditions and the hospitality extended to the Polish members of the team at the RCNP and the pleasant and efficient collaboration with the cyclotron team there.
References [1] [2] [3] [4] [5]
J. Eichler, Phys. Rep. 193 (1990) 165. Z. Sujkowski, Nucl. Phys. A 719 (2003) 266c. I. Katayama et al., Z. Phys. D 3 (1986) 73. I. Katayama et al., Phys. Rev. A 27 (1983) 2738. Y. Haruyama et al., Nucl. Instr. and Meth. B 33 (1988) 220. [6] N. Bohr, K. Dan, Vidensk. Selsk. Mat.-Fys. Medd. 18 (8) (1948) 1. [7] G.H. Gillespie, Phys. Rev. A 18 (1978) 1967. [8] G.H. Gillespie, Phys. Rev. A 26 (1982) 2421.
373
[9] J.R. Oppenheimer, Phys. Rev. 31 (1928) 349. [10] H.C. Brinkmann, H.A. Kramers, Proc. Acad. Sci. Amsterdam 33 (1930) 973. [11] M.R.C. McDowell, J.P. Coleman, Introduction to the Theory of Ion–atom Collisions, North–Holland, Amsterdam, 1970. [12] V.S. Nikolaev, Zh. Eksp. Theor. Fiz. 51 (1966) 1263. [13] G. Lapicki et al., Phys. Rev. A 22 (1980) 1896. [14] J. Eichler, Phys. Rev. A 32 (1985) 112. [15] J.A. Bearden, A.F. Burr, Rev. Mod. Phys. 39 (1967) 125. [16] K. Dennis et al., Phys. Rev. A 50 (1994) 3992. [17] M. Fujiwara et al., Nucl. Instr. and Meth. A 442 (1999) 484. [18] H. Akimune et al., Phys. Rev. C 52 (1995) 604. [19] D. Chmielewska et al., Proc. of the 8th International Conference on Nuclear Reaction Mechanisms, Varenna 1997; Ricerca Scientifica ed Educazione Permanente, p. 703; D. Chmielewska et al. Proc. of the International Winter Meeting on Nuclear Physics, Bormio 2000; Ricerca Scientifica ed Educazione Permanente Suppl. 116, p. 90.
Charge exchange processes for semi-relativistic helium ions (b = 0.51) in solid gold A. Go´jska a,*, D. Chmielewska a, J. Rzadkiewicz a, Z. Sujkowski a, T. Adachi b, H. Fujita b, Y. Fujita b, K. Hara b, Y. Haruyama b, J. Kamiya b, H. Ogawa b, M. Saito b, Y. Shimizu b, Y. Shimbara b, M. Tanaka b, H.P. Yoshida b, I. Katayama c The Andrzej Soltan Institute for Nuclear Studies, 05-400 Otwock–S´wierk, Poland b RCNP and Department of Physics, Osaka University, Japan IPNS (Institute of Particle and Nuclear Studies), KEK (High Energy Accelerator Research Organization) Oho 1, Tsukuba, Ibaraki 305-0801, Japan a
c
Available online 13 May 2005
Abstract Interactions of 150 MeV/amu 3He++ projectiles with solid gold targets have been studied at the isochronous cyclotron of the RCNP in Osaka. The 3He+ ions resulting from capture of the target electrons to the projectile were observed with the use of large magnetic spectrograph, Grand Raiden, set at h = 0 with respect to the beam. The yield ratio of singly to doubly ionized helium ions emerging from thin gold foils, He+/He++, has been measured as a function of the foil thickness. Extrapolating the results to zero Au target thickness permits to determine the cross section values for electron stripping from 3He+ ions, rSTRIP = 1.05 · 1017 cm2, and for electron capture to 3He++ ions, rCAP = 1.12 · 1025 cm2. The results obtained extend significantly the existing systematics for both processes to high (semi-relativistic) velocities. The collision strength deduced from the stripping cross sections deviates strongly from the theoretical predictions of Gillespie in absolute values as well as in the velocity dependence. It can, however, be well approximated by the simple Bohr formula for mid Z atoms. Also the capture data indicate the need to improve the theoretical approximations. A more detailed treatment of electrons captured from different shells in a high Z target is presumably needed. The astrophysical interest in the data of this kind for very light ions (hydrogen, helium) is indicated. 2005 Elsevier B.V. All rights reserved. PACS: 34.50.Fa; 34.70.+e Keywords: Charge exchange; Ionization (stripping); Capture
*
Corresponding author. Fax: +4822 779 34 81. E-mail address: [email protected] (A. Go´jska).
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.03.207
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
1. Introduction The dominant processes occurring to a fast ion traversing a solid are the capture of electrons from the target atoms to the vacant states in the ion and the stripping of the bound electrons from the ions. These charge exchange processes are of primary interest for understanding the passage of ions through matter. Though known and studied since the early days of atomic and sub-atomic physics, they are still only crudely described theoretically. The experimental information is also limited, particularly for light projectiles at intermediate and high (relativistic) energies. Because of huge differences in cross-sections between the capture and the stripping processes the experiments require very special techniques of advanced nuclear physics. The capture of electrons by an ion colliding with an atom proceeds via two processes: the Radiative Recombination, RR, and the NonRadiative Electron Capture, NREC. To the extent that the captured electron can be considered as free and at rest, the RR process corresponds to the Radiative Electron Capture, REC, which is the time reversed photo-electric effect on the partly ionized projectile atom. The NREC process cannot occur for free electrons. The momentum and energy conservation conditions require the presence of a third body, in this case the atomic nucleus of the target atom. The cross section, rNREC, depends sharply on the energy of the ion, EP, and on the atomic number of the target, ZT, as well as of the ion, ZP. It has a maximum close to the velocity matching condition, vp ve, where vp and ve are the velocities of the ion and the captured electron, respectively. For vp ve rNREC Z 5P Z 5T E6 P .
ð1Þ
Due to sharp ZT dependence the NREC process dominates for high Z targets and the total capture cross section, rCAP rNREC. In contrast, the ionization cross section, rSTRIP, depends smoothly on EP and Z. Crudely, rSTRIP
Z 2T 1 E . Z 2P P
ð2Þ
369
A review of the various processes occurring in the relativistic ion – atom collisions is given in [1] (see also [2] are Refs. therein). Recent experimental information on interaction of fast helium ions with various gaseous and solid targets can be found in the work of Katayama et al. [3–5]. These authors have measured the stripping and the capture cross section for 3He ions with energies up to 43.4 MeV/amu. The present work extends this information to much higher 3 He energy, 150 MeV/amu, for Z = 79. The results are compared with basic theories. Interaction of relativistic helium ions with atoms as well as with free electrons is of primary astrophysical interest [2]. Likewise, information on the charge exchange process involving fast ions is much needed in hot plasma diagnostics.
2. Theoretical predictions Collisions between fast ions and target atoms lead to electron capture to the vacant states in the ions. The impinging ions may also lose electrons in the ionization process, i.e. in the stripping of the bound electrons from the ion to the continuum. The ionization (stripping) process is described by Bohr [6] and Gillespie [7,8]. The electron capture cross section is given by the approximate calculations according to Oppenheimer–Brinkmann–Kramer [9–11] OBK, and Nikolaev [12,13] calculations. More realistic expressions in the relativistic eikonal approximation are given by Eichler [1,14]. The first description of electron ionization process was given by Bohr [6]. Three approximate expressions for the electron stripping were given for high, low and medium Z of target, correspondingly. The expression for high Z takes the particularly simple form rSTRIP ðhigh ZÞ pa20 .
ð3Þ
The Bohr predictions for mid Z targets include the screening effects due to tightly bound inner electrons 2=3 Z v0 rSTRIP ðmid ZÞ ¼ pa20 T ; ð3aÞ ZP v
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
370
where the Bohr radius a0 = 5.29 · 109 cm, the Bohr velocity v0 = 2,19 · 108 cm/s, v is the ion velocity, ZT is the atomic number of target and ZP is the atomic number of the projectile. The electron stripping cross section can be described by an asymptotic (high-speed) expansion form of the Born approximation. According to Gillespie [7,8] v 2 0 rSTRIP ¼ 8pa20 I ; ð4Þ v where the parameter I called the ionization collision strength is given by an integral over the momentum transfer 1.24 I 2 Z T ð1 þ 0.105Z T 5.4 104 Z 2T Þ. ð5Þ ZP A simple description of the NREC cross section is given by the OBK (Oppenheimer–Brinkmann– Kramer) theory which neglects the internuclear interaction in the perturbing potential. Only the interaction between the target electron and the incident ion is taken into account [1]. The cross section is expressed by the asymptotic equation 18 12 22 5 5 v0 rOBK Z ¼ pa Z . ð6Þ CAP 0 5 P T v The electron capture is a three body problem. The interaction between incident and target nuclei has to be taken into account. The electron capture cross section values calculated in the first order OBK approximation Eqs. (6) and (7) are larger than the experimental ones. The calculation in the second order B2 approximation [1]: v 5p 1 0 OBK rB2 ¼ r 0.295 þ ð7Þ CAP 211 Z P þ Z T v gives somewhat lower but still overestimated cross section values. A method to overcome these difficulties, proposed by Nikolaev [12], [13], included arbitrary external and internal screening corrections for the electron capture cross section from inner shells of the target to the vacant state in the ion 5 29 p n1 n2 2 v1s NIK rCAP ¼ n10 ðhÞ 5 v v2s
U4 ½ð1 hÞn2 ðhÞ ½1 þ ð1 hÞn2 ðhÞ
3
;
ð8Þ
where n1, n2 are quantum numbers of projectile and the target states, respectively, v1s = v0Z1/n1 and v2s = v0Z2eff/n2 are the orbital velocities of electron in the projectile and in the target, respectively, and v2s ffi; nðhÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð9Þ 2 v1s þ q2 ðhÞ Eb
with h ¼ Eii , Ebi is a binding energy taken from tables [15], Ei ¼ R Zneff2 .
Here qðhÞ ¼ 12 v þ v22s h v21s =v is the minimum momentum transfer.
3. Experiment Thin gold targets were bombarded with 150 MeV/amu 3He++ ions extracted from the ring cyclotron of the RCNP Osaka. The intensity ratio of singly to doubly ionized He ions leaving the target, R = Y(He+)/Y(He++), was measured as a function of the target thickness. In view of the rSTRIP value being about 108 times larger than rCAP this ratio is strongly thickness dependent. The yield of He+ ions corresponds to the survival probability of an ion which has captured an electron and escaped from the target prior to the subsequent electron stripping. At saturation, i.e. for x ! 1, R = rCAP/rSTRIP [16]. By fitting the function R = a[1exp(bx)] to the measured R(x) values we can obtain separately the relevant cross sections. Here a = rCAP/rSTRIP and b = rSTRIP. Singly ionized 3He+ ions together with tritons from the (3He, t) reaction were detected in the focal plane of the magnetic spectrometer Grand Raiden [17] set at h = 0 with respect to the beam, with vertical and horizontal angles of 40 mrad each. The 3He++ beam was fully intercepted by a Faraday cup placed in the first dipole magnet of the spectrometer. The set-up was identical to that used routinely by the Osaka group to study the Gamov–Teller strength distribution in the (3He, t) charge exchange reactions see e.g. [18]. Thin gold targets were prepared by evaporating gold onto 5 lg/cm2 thick carbon foils. The thicknesses of gold layers were measured in a separate scattering chamber with 5–10% accuracy. Targets 5.5, 9.6, 22.7 and 133.25 lg/cm2 thick were used.
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
The thick Au target of 1700 lg/cm2 was obtained commercially.
4. Results and discussion The measured yield ratio of the Y(3He+)/ Y( He++) versus the target thickness is presented in Fig. 1. The fitted cross section values are rSTRIP = (1.05 ± 0.19) · 1017 cm2 and rCAP = (1.12 ± 0.27) · 1025 cm2. The errors do not include uncertainties due to the possible surface contamination of the targets with light elements (carbon, oxygen). Approximate corrections for this effect lower the yield ratio values and introduce asymmetric errors to the final results. In order to reduce these errors the experiment was repeated several times for each target. The self– 3
Y( 3 He+ )/Y( 3 He ++)
150 MeV/amu 3He->Au 1.2x10
-8
8.0x10
-9
4.0x10
-9
0.0 10
100
1000 2
target thickness (µg/cm )
Fig. 1. The Y(3He+)/Y(3He++) yields as a function of target thickness for Au target. Points represent an experimental data. The curve show the results of fitting with Eq. (1).
cleansing effect of the beam on the target due to the sputtering of light impurities was sometimes observed. Only the ‘‘post-cleansing’’ data were included in the analysis. We attribute an additional 10% uncertainty to the final values to take the impurity effect into account. The existing data on the stripping cross section in the energy range 17.3–43.3 MeV/amu, supplemented by the present value at 150 MeV/amu, are collected in Table 1 and in Fig. 2. The theoretical values calculated according to formulae (3), (3a) and (4) are included for comparison. Table 2 presents essentially the same information in terms of the collision strength. This is illustrated in Fig. 3. It is seen that the Bohr (high Z) and the Gillespie approximations grossly overestimate the cross section values, while BohrÕs mid Z formula reproduces the data. This might indicate the importance of the screening effect even for the heavy, Z = 79, atom. The data for total capture cross sections for He interacting with gold are collected in Table 3 and illustrated with Fig. 4. A comparison of the data with the OBK, B2 and Nikolaev – type calculations shows that the first two overestimate the effect dramatically. Calculations according to Nikolaev reproduce the experiment at b = 0.51 (the present result) and deviate from the data at lower velocities up to about a factor four. Calculations following the eikonal approximation of Eichler [1] remain to be done before drawing detailed conclusions from this result. The present work is a part of a larger programme of studying charge exchange processes for high speed very light projectiles interacting
Table 1 The experimental and theoretical values of the ionization cross section of 3He+ interacting with Energy (MeV/amu)
b = v/c
17.3 20.5 24 33.1 43.4 150
0.19 0.21 0.23 0.26 0.29 0.51
79Au
at various projectile velocities
Stripping cross section * 1017 cm2 Experimental
3.51 2.96 2.93 2.37 1.66 1.05
(42) (35) (35) (28) (20) (19)
371
Ref.
Theoretical Bohr low Z
Bohr mid Z
Gillespie
79.7 67.4 57.8 43.8 34.4 11.5
3.06 2.82 2.61 2.27 2.01 1.17
14.6 12.4 10.6 8.04 6.32 2.12
[5] [5] [5] [3] [3] Present results
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
372
Fig. 2. The experimental (points) and calculated electron stripping cross section. The solid line is from calculations of Gillespie formula. The other are from Bohr approximation: dash line is for high Z, dotted line for mid Z and dash-dot is for low Z targets.
Fig. 3. Measured and calculated collision strength for 3 He ! Au at various projectile velocities. Solid line represents calculations using Bohr approximation for intermediate Z. The dotted line shows collision strength from Gillespie cross section.
Table 2 The experimental and theoretical values of the ionization cross section in terms of collision strength Energy (MeV/amu)
b = v/c Collision strength
Ref.
Experimental Theoretical Bohr Gillespie mid Z
17.3 20.5 24 33.1 43.4 150
0.19 0.21 0.23 0.26 0.29 0.51
34.76 34.70 40.12 42.81 38.3 71.95
30.37 33.02 34.15 40.98 46.24 79.87
147 147 147 147 147 147
[5] [5] [5] [3] [3] Present results
Fig. 4. The experimental (points) and calculated electron capture cross section. The solid line is from Nikolaev formula, dash line is from OBK and dotted line from B2 approximations.
with various targets (ranging from Z = 4 up to the heaviest targets available). Preliminary results for REC, NREC and stripping processes for Z = 6
target have been presented in [19]. Data for targets 6 < Z < 79 are being processed.
Table 3 The experimental and theoretical (OBK, B2 and Nikolaev) values of electron capture cross sections for 3He++ ! 79Au Energy (MeV/amu)
b = v/c
Electron capture cross section 1022 cm2 Experimental
22.6 33.1 43.4 150
0.22 0.26 0.29 0.51
1.41 (14) 0.413 (41) 0.202 (24) 0.00112 (27)
Ref.
Theoretical OBK
B2
Nikolaev
9710 1090 256 0.363
2860 321 75.5 0.107
0.374 0.125 0.0605 0.0010
[4] [4] [3] Present results
A. Go´jska et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 368–373
Acknowledgements We acknowledge with pleasure the excellent working conditions and the hospitality extended to the Polish members of the team at the RCNP and the pleasant and efficient collaboration with the cyclotron team there.
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