- Email: [email protected]
Condensed-state effects in pionic and muonic x-ray spectra
Volume Zi’A, number
PHYSICS
9
CONDENSED-STATE
EFFECTS
IN
23 September
LETTERS
PIONIC
AND
MUONIC
X-RAY
1968
SPECTRA
L. TAUSCHER *, G. BACKENSTOSS **, S. CHARALAMBUS, H. DANIEL *, H. KOCH **, G. POELZ and H. SCHMITT * CERN, Geneva, Switzerland,
Institut
fir
Max-Planck-Institut fir Kernphysik, Heidelberg, Germany, Experimentelle Kemphysik der Universitiit, Karlsruhe: Germany Received
Intensity measurements tion are reported.
12 August 1968
of pionic and muonic X-rays
in targets
of different
physical
or chemical
composi-
the Ca targets were prepared one day before the run. The Se targets were checked by X-ray diffraction analysis. The measurements were performed with Ge detectors at the CERN synchrocyclotron. A description of the set-up is given elsewhere [4]. Table 1 summarizes the experimental results. Column 1 contains the two transitions, whose intensity ratio is formed separately for each target Columns 2 through 6 show the ratio of the two intensitv ratios of the targets in comparison, e.g. in ihe fourth line of table 1.
Chemical effects were recently found in muonic X-ray spectra [l-3]. In an earlier paper [3] we reported data on such effects. In this letter we want to present results on intensity ratios measured with pions, and additional data for muons. The target pairs consisted of metallic and amorphous Se powder, CaO powder and granulated Ca, and TiO2 and Ti powder. The amorphous Se and * Max-Planck-Institut fiir Kernphysik, Heidelberg, Germans, and CERN, Geneva, Switzerland. ** Institut fib Experimentelle Kernphysik der Universitat, Karlsruhe, Germany, and CERN, Geneva, Switzerland.
Table 1 Experimental results.
(1)
(2)
I
(3)
Se amorphous’SemetaIlic
n
0.97 PO.13
5d-2p/3d-2p
i
4f -3d/3d-2p -3d
6f -3d/4f
-3d
1.02 * 0.04
(‘3)
(5)
CaO/Ca
r
P
4d-2pL3d-2p
5f -3d/4f
(4)
Ti02 /Ti
cc
n
0.86 * 0.07 1.01 f 0.14
1.21 f 0.05
0.89 f 0.05
1.05 f 0.04
0.74 f 0.06
0.99 f 0.08
0.95
0.06
0.92 * 0.03
0.92 f 0.10
0.83 f 0.06
1.47 * 0.12
0.84 f 0.06
7f -4f /4f -3d
l
0.94 * 0.14
5g-4f /4f -3d
0.92 * 0.03
0.83 f 0.07
1.06 f 0.10
6g-4f /5g-4f
1.03 * 0.04
1.10
0.93 * 0.09
7g-4f /5g-4f
1.17 * 0.09
1.29 f 0.19
ag-4f /5g-4f
1.09 f 0.12
1.07 5 0.21
7h-5g/5g-4f
0.97 f 0.06
0.90 f 0.28
6h-5g/7h-5g
0.96 f 0.15
l
0.08
L 581
Volume 27A. number 9
PHYSICS
LETTERS
23 September
1968
We thank the Batelle Institute, Geneva, and in particular Dr. Schachner, for X-ray diffraction analyses of the Se targets, and also CERN for its hospitality. for ?I and p, respectively. The values are corrected for self-absorption. The errors are standard deviations. If there were no effects, all the numbers listed in the table would be unity. Effects are evident for all target pairs; these effects are usually stronger for muons than for pions. The most interesting case is that of Se, where the targets differ only in their physical form. Measurements with a Se target which consisted mostly of Se in monoclinic form give, for some transition ratios, even stronger effects than those obtained with amorphous Se. The results are not listed in table 1 because of uncertainties in the target composition. For a discussion of the condensed-state effects we refer to earlier papers [3,5].
References 1. V.G.Zinov. 2.
3. 4. 5.
A.D.Konin, A.I.MukhinandR.V.Polyakova. Yadern. Fiz. 5 (1967) 591; Soviet J. Nucl. Phys. 5 (1967) 420. D.Kessler, H. L.Anderson, M.S.Dixit. H. J.Evans. R. J. McKee, C.K. Hargrove, R.D.Barton, E. P. Hincks and J.D.McAndrew, Phrs. Rev. Letters 18 (1967) 1179. H.Daniel. H.Koch, G. Poelz, H.Schmitt. L.Tauschei G. Backenstoss and S. Charalambus. Phys. Letters 26B (1968) 281. H.Daniel. G. Poelz, H.Schmitt. G.Backenstoss. H. Koch and S.Charalambus. Z. Phys. 205 (1967) 472. H.Daniel. Naturwissenschaften 55 (1968) 314.
**+**
INTERFERENCE ON PROTONS
EFFECTS IN NEUTRON IN A DOUBLE MINIMUM
SCATTERING POTENTIAL
C. SCHENK and B. WECKERMANN Dizjisionof Experimental Neutron Physics I Department of Reactor Physics, Euratom? Joint Research Received
Center,
Ispra. Italy
12 August 1968
Based on the theoretical treatments by Stiller and Stamenkovich of the incoherent neutron scattering at a proton in a double minimum potential well experiments had been performed with KH2P04 single crystals to prove the predicted interference effect.
Stiller [l] and lately Stamenkovich [2] have shown that neutrons which are scattered truly elastically and incoherently by protons tunneling in a double minimum potential well, should show an intereference effect. KH2PO4 single crystals are most suitable for an experimental proof, as the hydrogen bonds are oriented along the x and y axis [3]. Therefore the ratio V of scattered intensity with x vector parallel to the x-axis to the one with 1~vector parallel to the z axis is a sensitive quantity to possible interference effects. (x stands for momentum transfer). In order to distinguish between an anisotropic single well potential and a double minimum potential we dis582
cuss the /x 1 dependence of the ratio V. Assuming a harmonic oscillator with the m 9jm squgre displacement $ along the bond and Ub and uc perpendicular to it, the ratio V is given by ‘harm
J
=z
exp =
t-x2utj +exp (-x2+
2 exp(-x2u2)c ’ In fig. 1 tiharm is plotted as full line for ub = uc and fitted to a measurem nt recently done by Stiller [4] at (X / = 5.5A- ‘i . For the case of the double minimum potential well, one obtains according to Stiller [l] for the scattering law:
PHYSICS
9
CONDENSED-STATE
EFFECTS
IN
23 September
LETTERS
PIONIC
AND
MUONIC
X-RAY
1968
SPECTRA
L. TAUSCHER *, G. BACKENSTOSS **, S. CHARALAMBUS, H. DANIEL *, H. KOCH **, G. POELZ and H. SCHMITT * CERN, Geneva, Switzerland,
Institut
fir
Max-Planck-Institut fir Kernphysik, Heidelberg, Germany, Experimentelle Kemphysik der Universitiit, Karlsruhe: Germany Received
Intensity measurements tion are reported.
12 August 1968
of pionic and muonic X-rays
in targets
of different
physical
or chemical
composi-
the Ca targets were prepared one day before the run. The Se targets were checked by X-ray diffraction analysis. The measurements were performed with Ge detectors at the CERN synchrocyclotron. A description of the set-up is given elsewhere [4]. Table 1 summarizes the experimental results. Column 1 contains the two transitions, whose intensity ratio is formed separately for each target Columns 2 through 6 show the ratio of the two intensitv ratios of the targets in comparison, e.g. in ihe fourth line of table 1.
Chemical effects were recently found in muonic X-ray spectra [l-3]. In an earlier paper [3] we reported data on such effects. In this letter we want to present results on intensity ratios measured with pions, and additional data for muons. The target pairs consisted of metallic and amorphous Se powder, CaO powder and granulated Ca, and TiO2 and Ti powder. The amorphous Se and * Max-Planck-Institut fiir Kernphysik, Heidelberg, Germans, and CERN, Geneva, Switzerland. ** Institut fib Experimentelle Kernphysik der Universitat, Karlsruhe, Germany, and CERN, Geneva, Switzerland.
Table 1 Experimental results.
(1)
(2)
I
(3)
Se amorphous’SemetaIlic
n
0.97 PO.13
5d-2p/3d-2p
i
4f -3d/3d-2p -3d
6f -3d/4f
-3d
1.02 * 0.04
(‘3)
(5)
CaO/Ca
r
P
4d-2pL3d-2p
5f -3d/4f
(4)
Ti02 /Ti
cc
n
0.86 * 0.07 1.01 f 0.14
1.21 f 0.05
0.89 f 0.05
1.05 f 0.04
0.74 f 0.06
0.99 f 0.08
0.95
0.06
0.92 * 0.03
0.92 f 0.10
0.83 f 0.06
1.47 * 0.12
0.84 f 0.06
7f -4f /4f -3d
l
0.94 * 0.14
5g-4f /4f -3d
0.92 * 0.03
0.83 f 0.07
1.06 f 0.10
6g-4f /5g-4f
1.03 * 0.04
1.10
0.93 * 0.09
7g-4f /5g-4f
1.17 * 0.09
1.29 f 0.19
ag-4f /5g-4f
1.09 f 0.12
1.07 5 0.21
7h-5g/5g-4f
0.97 f 0.06
0.90 f 0.28
6h-5g/7h-5g
0.96 f 0.15
l
0.08
L 581
Volume 27A. number 9
PHYSICS
LETTERS
23 September
1968
We thank the Batelle Institute, Geneva, and in particular Dr. Schachner, for X-ray diffraction analyses of the Se targets, and also CERN for its hospitality. for ?I and p, respectively. The values are corrected for self-absorption. The errors are standard deviations. If there were no effects, all the numbers listed in the table would be unity. Effects are evident for all target pairs; these effects are usually stronger for muons than for pions. The most interesting case is that of Se, where the targets differ only in their physical form. Measurements with a Se target which consisted mostly of Se in monoclinic form give, for some transition ratios, even stronger effects than those obtained with amorphous Se. The results are not listed in table 1 because of uncertainties in the target composition. For a discussion of the condensed-state effects we refer to earlier papers [3,5].
References 1. V.G.Zinov. 2.
3. 4. 5.
A.D.Konin, A.I.MukhinandR.V.Polyakova. Yadern. Fiz. 5 (1967) 591; Soviet J. Nucl. Phys. 5 (1967) 420. D.Kessler, H. L.Anderson, M.S.Dixit. H. J.Evans. R. J. McKee, C.K. Hargrove, R.D.Barton, E. P. Hincks and J.D.McAndrew, Phrs. Rev. Letters 18 (1967) 1179. H.Daniel. H.Koch, G. Poelz, H.Schmitt. L.Tauschei G. Backenstoss and S. Charalambus. Phys. Letters 26B (1968) 281. H.Daniel. G. Poelz, H.Schmitt. G.Backenstoss. H. Koch and S.Charalambus. Z. Phys. 205 (1967) 472. H.Daniel. Naturwissenschaften 55 (1968) 314.
**+**
INTERFERENCE ON PROTONS
EFFECTS IN NEUTRON IN A DOUBLE MINIMUM
SCATTERING POTENTIAL
C. SCHENK and B. WECKERMANN Dizjisionof Experimental Neutron Physics I Department of Reactor Physics, Euratom? Joint Research Received
Center,
Ispra. Italy
12 August 1968
Based on the theoretical treatments by Stiller and Stamenkovich of the incoherent neutron scattering at a proton in a double minimum potential well experiments had been performed with KH2P04 single crystals to prove the predicted interference effect.
Stiller [l] and lately Stamenkovich [2] have shown that neutrons which are scattered truly elastically and incoherently by protons tunneling in a double minimum potential well, should show an intereference effect. KH2PO4 single crystals are most suitable for an experimental proof, as the hydrogen bonds are oriented along the x and y axis [3]. Therefore the ratio V of scattered intensity with x vector parallel to the x-axis to the one with 1~vector parallel to the z axis is a sensitive quantity to possible interference effects. (x stands for momentum transfer). In order to distinguish between an anisotropic single well potential and a double minimum potential we dis582
cuss the /x 1 dependence of the ratio V. Assuming a harmonic oscillator with the m 9jm squgre displacement $ along the bond and Ub and uc perpendicular to it, the ratio V is given by ‘harm
J
=z
exp =
t-x2utj +exp (-x2+
2 exp(-x2u2)c ’ In fig. 1 tiharm is plotted as full line for ub = uc and fitted to a measurem nt recently done by Stiller [4] at (X / = 5.5A- ‘i . For the case of the double minimum potential well, one obtains according to Stiller [l] for the scattering law: