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Projectile fluorescence yields in heavy ion collisions
Volume
67A, number
2
PHYSICS
LETTERS
24 July 1978
PROJECTILE FLUORESCENCE YIELDS IN HEAVY ION COLLISIONS *
J.A. TANIS ’ and S.M. SHAFROTH Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 2 7514, USA and Triangle Universities Nuclear Laboratory, Durham, NC 2 7706, USA Received
21 November
1977
Fluorescence yields of highly ionized projectiles entering thin solid foils are determined from a target-thickness analysis of projectile and target K X-ray cross sections. Values are obtained for 20-80 MeV Cl ions on Cu and compared with scaling calculations.
Previous experimental work [l-4] on fluorescence yields in heavy ion collisions has been done primarily with gas targets. Auger electron and K X-ray cross sections are obtained and the fluorescence yield is given by UK = ax/(ox t oA). Recent calculations [S] have shown how fluorescence yields depend on the state of multiple ionization and detailed coupling of electrons making the transitions. In this letter we show how the K-shell fluorescence yields of a heavy ion projectile entering a thin metal foil can be determined by extrapolating target and projectile K X-ray yields to zero target thickness. This eliminates the need to measure Auger electron cross sections. Target and projectile K X-rays were detected for 20-80 MeV Cl9+ ions incident on thin self-supporting Cu (60-220 pg/cm2) and Cu K X-rays were detected for carbon-backed Cu targets down to 25 pg/cm2. At 80 MeV data were taken for charge states 10 and 16 [7]. The resulting target and projectile X-ray cross sections for 60 MeV C18+ on Cu are shown in fig. 1. The solid curves through the data points are the results of a least squares analysis similar to that described by Gray et al. [8] and are based on the model of Betz et * Work supported in part by the U.S. Energy Research and Deveiopment Administration and by a grant from the North Carolina Board of Science and Technology. ’ Present address: Physics Department, East Carolina University, Greenville, NC 27834.
124
Cl
0
K
X-RAYS
40
120
80
160
200
240
X(pg/cm*)
Fig. 1. Projectile and target K X-ray production cross sections versus target thickness for 60 MeV Cl ions incident on thin self-supporting Cu targets. The curve through the target X-ray data is the result of a least squares fit to eq. (2) with A= 0. The curve through the projectile data is the result of a similar analysis [ 71 which takes into account X-ray production inside and outside the foil.
al. [9]. It is observed experimentally [8,10] that a projectile with a K vacancy produces a large enhancement in the measured target K X-ray production cross section which, for a foil of thickness T, is given by T 1
~~(T)=~~(o:oYo+~txlY1)dx, 0
(1)
Volume 67A, number 2
24 July 1978
PHYSICS LETTERS
Table 1 Values of projectile X-ray cross sections o%O for vanishing target thickness and projectge vacancy production cross sections o,‘obtamed from least squares fits to the data [6,7]. The experimental fluorescence yield wk was calculated from the ratio &/ov. iiL is the estimated average number of L vacancies present at X-ray emission [ 161. The theoretical WOK values are scaled estimates of the fluorescence yield (Larkins [ 171) and Greenberg et al. [18]. E
(a - 1) ova)
(MeV)
(kb)
20 40 60 80
8200 6300 2560 _
(o-
;;b)
P e) cxo (kb)
86.4 296 360 350 d)
11.3 88.7 151 231
1)
94.9 b) 21.3 b) 7.1 c) 4.6 d)
ifLfJ
4
(scaled) 0.13 0.30 0.42 0.66
3.2 4.6 5.5 6.1
0.16 0.23 0.33 0.45
a) Values obtained from least squares fit of data [6]. b, Calculated from eq. (4) (see text). ‘) Experimental value from Gray et al. [8]. d, Experimental value from Tanis et al. [ 71. e, From exponential least squares fit to projectile X-rays [7]. f) From comparison of the measured projectile Karenergy shifts from the values of Bearden [ 191 with the calculated shifts using the HFS computer code of Herman and Skillman [ 201. where ok0 and u&I are the target K X-ray production cross sections due to projectiles without and with a K vacancy (t denotes target X-ray cross sections) and Ye(x) and Yl (x) are the fraction of projectiles without and with a K vacancy at a depth x in the foil. Letting 0x1= “cJ;o where a! > 1 (a is a function of incident energy) and considering the exponential behaviour of Y, and Yo, one obtains [8]
Zfx(T>= uXo l+(a-1); [ -%[;-/I]
(W)],
(2)
where uv is the vacancy production cross section for the projectile, and u = uv + uc t u,, where u, and cr7 are electron capture and quenching cross sections (radiative and Auger) for the projectile. A is the fraction of incident ions with single K vacancies. (Double K vacancies are so rare at these bombarding energies as to be negligible.) Eq. (2) can be used to perform a least squares fit to the target X-ray production data giving values for the parameters ufxo, (Y,uv and u. The parameter of interest here is u,, the K-vacancy production cross section in the projectile. If, however, X-ray production is measured only for A = 0 (4 < 2, - 2) then only the product (o- l)‘o, is obtained. In the present work A = 0 for the 20,40 and 60 MeV data, while for 80 MeV data were taken for both A =O and A = 1.
A similar analysis, taking into account X-ray production both inside and outside the foil, was applied to the projectile X-ray data as a function of target thickness. An exponential function was fit to these data giving values for agO, the projectile X-ray cross section for vanishing target thickness. It is assumed that ugo does not depend on the incident charge state for 4 < ZI - 2 thereby requiring that electrons in shells higher than the K-shell reach charge state equilibrium very rapidly (in the first few atomic layers) after entry into the foil. The recent work of Cocke et al. [I l] shows. this to be a reasonable assumption. Thus the quantity ugo is the K X-ray production cross section for a projectile with no initial K vacancies and an equilibrium charge distribution in the higher shells. These results can be used to determine the projectile fluorescence yield WL which is given by ,i
K
= u~ lo x0 v’
(3)
Since the least squares tit to the target X-ray data for A = 0 (20,40 and 60 MeV Cl projectiles) gave values only for the product (LY- l)u,, it was necessary to determine (Yin order to calculate u,. For 60 MeV we used the experimental value of (Yfound by Gray et al. [8]. Furthermore, these authors find that the factor (Ycan be calculated quite accurately according to the formula (see also Gardner et al. [12]): (Y- 1 = rrR2wwCu/u~o
,
(4) 125
Volume 67A, number 2
PHYSICS LETTERS
24 July 1978
tal data is obtained but the theoretical curve differs systematically in magnitude from the experimental values, especially as 2, increases. This is most likely due to inherent inaccuracies in the scaling procedure used to calculate wk. In conclusion we have shown that the measurement of both target and projectile X-ray production cross sections as a function of target thickness can be used to determine the fluorescence yield for highly ionized projectiles in collisions with thin solid targets.
0.6 Cl WI
Helpful discussions with W.J. Thompson, J.P. Rozet and A. Kodre concerning the data analysis are gratefully acknowledged. [ 1] P. Richard, Atomic inner shell processes, ed. B. Crasemann
0.00
E (MeV)
Fig. 2. Fluorescence yield wk for 20-80 MeV Cl ions incident on Cu. The scale along the top gives the average number of L vacancies, i?L, for the range of energies investigated here. A fully stripped M-shell is assumed. The solid line through the data is drawn to guide the eye. The single vacancy fluorescence yield is taken from Bambynek et al. [ 2 11. The dashed curve is a scaled theoretical estimate of the fluorescence yield (Larkins [ 171 and Greenberg et al. [ 181).
where R is the radius corresponding to the peak in the dynamic coupling matrix elements as given by Taulbjerg et al. [ 13 1, w is the vacancy transfer probability (Meyerhof [ 14]), and wcu is the single vacancy fluorescence yield for Cu. The helium-like binding energy (Kelly and Harrison [ 151) for the Cl K-shell was used in the calculation of w. For 20 and 40 MeV Cl projectiles (Ywas calculated according to this formula, thus allowing a determination of uv. The results of the above analysis are summarized in table 1 and plotted in fig. 2. The table indicates the average number of L vacancies, ZL, corresponding to each of the incident energies [ 161. Scaled values for ok (EL) were computed by methods of Larkins 1171 and Greenberg et al. [ 181. It is observed that o&has a value close to the single vacancy value [2 l] for 20 MeV Cl but increases by a factor of about six for 80 MeV Cl. Also shown in the figure are the scaled theoretical estimates of the fluorescence yield for increasing numbers of L vacancies, ZL. Qualitative agreement with the trend of the experimen126
(Academic Press, 1975) Ch. 2. [2] D. Schneider, N. Stolterfoht, D.L. Matthews and F. Hopkins, Intern. Conf. on the Physics of electronic and atomic collisions (ICPEAC) X, Abstracts (1977) p. 200. [3] V.V. Afrosimov, Y??..Gordeev, A.N. Zinoviev, G.G. Me&hi and A.P. Shergin, ICPEAC X, Abstracts (1977) p. 202. [4] J.R. MacDonald, ICPEAC IX, Invited Lectures (1975) p. 408; B.L. Doyle, U. Schiebel, J.R. Macdonald and L.D. Elsworth, preprint (1977). [5] B. Crasemann and M.H. Chen, ICPEAC X, Abstracts (1977) p. 206; C.P. Bhalla, J. Phys. B8 (1975) 2787. [6] J.A. Tanis, J.M. Feagin, S.M. Shafroth and D. Schneider, ICPEAC X, Abstracts (1977) p. 342; J.A. Tanis, W.W. Jacobs and S.M. Shafroth, Bull. Am. Phys. Sot. 22 (1977) 625. [7] J.A. Tanis, S.M. Shafroth, T. Ainsworth and J. Willis, Bull. Am. Phys. Sot. (Knoxville meeting, 1977). [8] T.J. Gray, P. Richard, K.A. Jamison and J.M. Hall, Phys. Rev. Al4 (1977) 1333. [9] H.-D. Betz et al., Phys. Rev. Lett. 33 (1974) 807. [lo] F. Hopkins, Phys. Rev. Lett. 35 (1975) 270. [ 1 l] C.L. Cocke, S.L. Varghese and B. Curnutte, Phys. Rev. Al5 (1977) 874. [12] R.K. Gardner et al., Phys. Rev. Al5 (1977) 2202. [13] K. Taulbjerg, J. Vaaben and B. Fastrup, Phys. Rev. Al2 (1975) 2325. [14] W.E. Meyerhof, Phys. Rev. Lett. 31 (1973) 1341. [15] R.L. Kelly and D.E. Harrison, At. Data 3 (1973) 177. [16] E. Drane, J.M. Feagin, S.M. Shafroth and J.A. Tanis, Bull. Am. Phys. Sot. (Knoxville meeting, 1977) (describes the method of estimating TTL). [17] F.P. Larkins, J. Phys. B4 (1971) L29. 1181 J.S. Greenberg, P. Vincent and W. Lichten, Phys. Rev. Al6 (1977) 964. [19] F. Herman and S. Skillman, Atomic structure calculations (Prentice-Hall, Englewood Cliffs, NJ, 1963); [20] W. Bambynek et al., Rev. Mod. Phys. 44 (1972) 716.
67A, number
2
PHYSICS
LETTERS
24 July 1978
PROJECTILE FLUORESCENCE YIELDS IN HEAVY ION COLLISIONS *
J.A. TANIS ’ and S.M. SHAFROTH Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 2 7514, USA and Triangle Universities Nuclear Laboratory, Durham, NC 2 7706, USA Received
21 November
1977
Fluorescence yields of highly ionized projectiles entering thin solid foils are determined from a target-thickness analysis of projectile and target K X-ray cross sections. Values are obtained for 20-80 MeV Cl ions on Cu and compared with scaling calculations.
Previous experimental work [l-4] on fluorescence yields in heavy ion collisions has been done primarily with gas targets. Auger electron and K X-ray cross sections are obtained and the fluorescence yield is given by UK = ax/(ox t oA). Recent calculations [S] have shown how fluorescence yields depend on the state of multiple ionization and detailed coupling of electrons making the transitions. In this letter we show how the K-shell fluorescence yields of a heavy ion projectile entering a thin metal foil can be determined by extrapolating target and projectile K X-ray yields to zero target thickness. This eliminates the need to measure Auger electron cross sections. Target and projectile K X-rays were detected for 20-80 MeV Cl9+ ions incident on thin self-supporting Cu (60-220 pg/cm2) and Cu K X-rays were detected for carbon-backed Cu targets down to 25 pg/cm2. At 80 MeV data were taken for charge states 10 and 16 [7]. The resulting target and projectile X-ray cross sections for 60 MeV C18+ on Cu are shown in fig. 1. The solid curves through the data points are the results of a least squares analysis similar to that described by Gray et al. [8] and are based on the model of Betz et * Work supported in part by the U.S. Energy Research and Deveiopment Administration and by a grant from the North Carolina Board of Science and Technology. ’ Present address: Physics Department, East Carolina University, Greenville, NC 27834.
124
Cl
0
K
X-RAYS
40
120
80
160
200
240
X(pg/cm*)
Fig. 1. Projectile and target K X-ray production cross sections versus target thickness for 60 MeV Cl ions incident on thin self-supporting Cu targets. The curve through the target X-ray data is the result of a least squares fit to eq. (2) with A= 0. The curve through the projectile data is the result of a similar analysis [ 71 which takes into account X-ray production inside and outside the foil.
al. [9]. It is observed experimentally [8,10] that a projectile with a K vacancy produces a large enhancement in the measured target K X-ray production cross section which, for a foil of thickness T, is given by T 1
~~(T)=~~(o:oYo+~txlY1)dx, 0
(1)
Volume 67A, number 2
24 July 1978
PHYSICS LETTERS
Table 1 Values of projectile X-ray cross sections o%O for vanishing target thickness and projectge vacancy production cross sections o,‘obtamed from least squares fits to the data [6,7]. The experimental fluorescence yield wk was calculated from the ratio &/ov. iiL is the estimated average number of L vacancies present at X-ray emission [ 161. The theoretical WOK values are scaled estimates of the fluorescence yield (Larkins [ 171) and Greenberg et al. [18]. E
(a - 1) ova)
(MeV)
(kb)
20 40 60 80
8200 6300 2560 _
(o-
;;b)
P e) cxo (kb)
86.4 296 360 350 d)
11.3 88.7 151 231
1)
94.9 b) 21.3 b) 7.1 c) 4.6 d)
ifLfJ
4
(scaled) 0.13 0.30 0.42 0.66
3.2 4.6 5.5 6.1
0.16 0.23 0.33 0.45
a) Values obtained from least squares fit of data [6]. b, Calculated from eq. (4) (see text). ‘) Experimental value from Gray et al. [8]. d, Experimental value from Tanis et al. [ 71. e, From exponential least squares fit to projectile X-rays [7]. f) From comparison of the measured projectile Karenergy shifts from the values of Bearden [ 191 with the calculated shifts using the HFS computer code of Herman and Skillman [ 201. where ok0 and u&I are the target K X-ray production cross sections due to projectiles without and with a K vacancy (t denotes target X-ray cross sections) and Ye(x) and Yl (x) are the fraction of projectiles without and with a K vacancy at a depth x in the foil. Letting 0x1= “cJ;o where a! > 1 (a is a function of incident energy) and considering the exponential behaviour of Y, and Yo, one obtains [8]
Zfx(T>= uXo l+(a-1); [ -%[;-/I]
(W)],
(2)
where uv is the vacancy production cross section for the projectile, and u = uv + uc t u,, where u, and cr7 are electron capture and quenching cross sections (radiative and Auger) for the projectile. A is the fraction of incident ions with single K vacancies. (Double K vacancies are so rare at these bombarding energies as to be negligible.) Eq. (2) can be used to perform a least squares fit to the target X-ray production data giving values for the parameters ufxo, (Y,uv and u. The parameter of interest here is u,, the K-vacancy production cross section in the projectile. If, however, X-ray production is measured only for A = 0 (4 < 2, - 2) then only the product (o- l)‘o, is obtained. In the present work A = 0 for the 20,40 and 60 MeV data, while for 80 MeV data were taken for both A =O and A = 1.
A similar analysis, taking into account X-ray production both inside and outside the foil, was applied to the projectile X-ray data as a function of target thickness. An exponential function was fit to these data giving values for agO, the projectile X-ray cross section for vanishing target thickness. It is assumed that ugo does not depend on the incident charge state for 4 < ZI - 2 thereby requiring that electrons in shells higher than the K-shell reach charge state equilibrium very rapidly (in the first few atomic layers) after entry into the foil. The recent work of Cocke et al. [I l] shows. this to be a reasonable assumption. Thus the quantity ugo is the K X-ray production cross section for a projectile with no initial K vacancies and an equilibrium charge distribution in the higher shells. These results can be used to determine the projectile fluorescence yield WL which is given by ,i
K
= u~ lo x0 v’
(3)
Since the least squares tit to the target X-ray data for A = 0 (20,40 and 60 MeV Cl projectiles) gave values only for the product (LY- l)u,, it was necessary to determine (Yin order to calculate u,. For 60 MeV we used the experimental value of (Yfound by Gray et al. [8]. Furthermore, these authors find that the factor (Ycan be calculated quite accurately according to the formula (see also Gardner et al. [12]): (Y- 1 = rrR2wwCu/u~o
,
(4) 125
Volume 67A, number 2
PHYSICS LETTERS
24 July 1978
tal data is obtained but the theoretical curve differs systematically in magnitude from the experimental values, especially as 2, increases. This is most likely due to inherent inaccuracies in the scaling procedure used to calculate wk. In conclusion we have shown that the measurement of both target and projectile X-ray production cross sections as a function of target thickness can be used to determine the fluorescence yield for highly ionized projectiles in collisions with thin solid targets.
0.6 Cl WI
Helpful discussions with W.J. Thompson, J.P. Rozet and A. Kodre concerning the data analysis are gratefully acknowledged. [ 1] P. Richard, Atomic inner shell processes, ed. B. Crasemann
0.00
E (MeV)
Fig. 2. Fluorescence yield wk for 20-80 MeV Cl ions incident on Cu. The scale along the top gives the average number of L vacancies, i?L, for the range of energies investigated here. A fully stripped M-shell is assumed. The solid line through the data is drawn to guide the eye. The single vacancy fluorescence yield is taken from Bambynek et al. [ 2 11. The dashed curve is a scaled theoretical estimate of the fluorescence yield (Larkins [ 171 and Greenberg et al. [ 181).
where R is the radius corresponding to the peak in the dynamic coupling matrix elements as given by Taulbjerg et al. [ 13 1, w is the vacancy transfer probability (Meyerhof [ 14]), and wcu is the single vacancy fluorescence yield for Cu. The helium-like binding energy (Kelly and Harrison [ 151) for the Cl K-shell was used in the calculation of w. For 20 and 40 MeV Cl projectiles (Ywas calculated according to this formula, thus allowing a determination of uv. The results of the above analysis are summarized in table 1 and plotted in fig. 2. The table indicates the average number of L vacancies, ZL, corresponding to each of the incident energies [ 161. Scaled values for ok (EL) were computed by methods of Larkins 1171 and Greenberg et al. [ 181. It is observed that o&has a value close to the single vacancy value [2 l] for 20 MeV Cl but increases by a factor of about six for 80 MeV Cl. Also shown in the figure are the scaled theoretical estimates of the fluorescence yield for increasing numbers of L vacancies, ZL. Qualitative agreement with the trend of the experimen126
(Academic Press, 1975) Ch. 2. [2] D. Schneider, N. Stolterfoht, D.L. Matthews and F. Hopkins, Intern. Conf. on the Physics of electronic and atomic collisions (ICPEAC) X, Abstracts (1977) p. 200. [3] V.V. Afrosimov, Y??..Gordeev, A.N. Zinoviev, G.G. Me&hi and A.P. Shergin, ICPEAC X, Abstracts (1977) p. 202. [4] J.R. MacDonald, ICPEAC IX, Invited Lectures (1975) p. 408; B.L. Doyle, U. Schiebel, J.R. Macdonald and L.D. Elsworth, preprint (1977). [5] B. Crasemann and M.H. Chen, ICPEAC X, Abstracts (1977) p. 206; C.P. Bhalla, J. Phys. B8 (1975) 2787. [6] J.A. Tanis, J.M. Feagin, S.M. Shafroth and D. Schneider, ICPEAC X, Abstracts (1977) p. 342; J.A. Tanis, W.W. Jacobs and S.M. Shafroth, Bull. Am. Phys. Sot. 22 (1977) 625. [7] J.A. Tanis, S.M. Shafroth, T. Ainsworth and J. Willis, Bull. Am. Phys. Sot. (Knoxville meeting, 1977). [8] T.J. Gray, P. Richard, K.A. Jamison and J.M. Hall, Phys. Rev. Al4 (1977) 1333. [9] H.-D. Betz et al., Phys. Rev. Lett. 33 (1974) 807. [lo] F. Hopkins, Phys. Rev. Lett. 35 (1975) 270. [ 1 l] C.L. Cocke, S.L. Varghese and B. Curnutte, Phys. Rev. Al5 (1977) 874. [12] R.K. Gardner et al., Phys. Rev. Al5 (1977) 2202. [13] K. Taulbjerg, J. Vaaben and B. Fastrup, Phys. Rev. Al2 (1975) 2325. [14] W.E. Meyerhof, Phys. Rev. Lett. 31 (1973) 1341. [15] R.L. Kelly and D.E. Harrison, At. Data 3 (1973) 177. [16] E. Drane, J.M. Feagin, S.M. Shafroth and J.A. Tanis, Bull. Am. Phys. Sot. (Knoxville meeting, 1977) (describes the method of estimating TTL). [17] F.P. Larkins, J. Phys. B4 (1971) L29. 1181 J.S. Greenberg, P. Vincent and W. Lichten, Phys. Rev. Al6 (1977) 964. [19] F. Herman and S. Skillman, Atomic structure calculations (Prentice-Hall, Englewood Cliffs, NJ, 1963); [20] W. Bambynek et al., Rev. Mod. Phys. 44 (1972) 716.