Chapter 1 Level Crossing

Transcription

1 Chapter 1 Level Crossing When I arrived at MIT in the summer of 1955, I was assigned as a research assistant in the group of Professor Francis Bitter, who was a kind and extremely supportive adviser to all his students. Bitter was well known as a leader in magnetism and in the mid 1930s established at MIT a facility where high magnetic fields were available for studying the susceptibility and other properties of materials. The magnets, of his own design, could reach 5 Tesla in a 4-inch diameter bore, by carrying large currents provided from a bank of submarine batteries [1]. After service with the US Navy during World War II, Bitter returned to MIT where he carried out a series of nuclear magnetic resonance experiments, and became interested in using the same principle in atomic systems. This led to the double resonance techniques which was first correctly formulated by A. Kastler of the College de France [2]. The first experiment was carried out by Jean Brossel, a former student of Kastler, and by then a doctoral student in Bitter s lab [3]. When I joined the group it consisted of four fairly experienced graduate students, Bert Aubrey, Dick Lacey, Jack Stanley and Norman Adams, and a recent graduate, Paul Sagalyn, who would occasionally come to help us; there was also a close connection with the MIT atomic spectroscopy lab. The effort of the group was on the double resonance technique, to be explained below, in order to measure atomic hyperfine structure, and thereby extract from the 1

2 2 Reminiscences: A Journey Through Particle Physics data precise values of nuclear magnetic moments. I inherited the working apparatus that Sagalyn had used in his thesis, and was therefore able to obtain new results in a short time, but without fully understanding the subtle details of the theoretical framework. For my thesis, I was to study Mercury-197 ( 197 Hg), a radioactive isotope of Mercury that also had an excited nuclear isomeric state, 197 Hg of sufficiently long lifetime such that it could be subjected to double resonance and to spectroscopic investigations. It was during this work that serendipity led me and our laboratory technician to consider level crossing in atomic systems. We made a lame attempt to detect the effect, but failed because we did not appreciate its full significance. However, to tell this story, we must first discuss in some detail the basics of double resonance experiments. Mercury has 80 electrons, two of which are outside of the closed shells and therefore determine its atomic spectrum. The spectral line that we studied was the well known UV line at λ = 253.7nm,whichis very strongly emitted in a Hg discharge, and is also easily excited by resonance radiation. It arises from the transition of the excited 6 3 P 1 state to the 6 1 S 0 ground state. The spectroscopic notation implies that the excited state has orbital angular momentum L = 1 (hence P - state), total spin S = 1 (hence triplet), and total angular momentum J = 1 (subscript). The low lying excited states and spectral lines are showninfig.1.1(a). Natural Hg contains several isotopes, and the size and the magnetic dipole (and electric quadrupole) moment of the nucleus, when different from zero, affect the energy of the spectral lines arising from the transition of the 3 P 1 to the ground state. For isotopes with an even number of nucleons, the nuclear spin is zero, and the spectra differ only by their corresponding isotope shift. However 199 Hg and 201 Hg have nuclear spin I =1/2 andi =3/2 respectively, which are coupled to the total electronic angular momentum J, giving rise to a new quantum number F that labels the vectorial sum of I and J. For a given value of J, andwheni < J,thereare2I +1 F - levels as a consequence of the coupling of the nuclear moments to the total electronic angular momentum; when J<Ithe number of levels is 2J +1. This gives rise, in addition to the isotope shift, to the

3 Level Crossing 3 Figure 1.1: (a) The spectrum of lines emitted in the transitions of the low-lying states of Hg. Wavelengths are given in Å, where1å =10 10 m. (b) The hyperfine structure of the nm line, arising from the transition 3 P 1 1 S 0 in natural Hg [3]. hyperfine structure of the spectral line. The structure of the nm line of natural Hg is shown a in Fig. 1.1(b). Energy differences are given in spectroscopic units of inverse length, κ = E/hc = ν/c, so that 1 cm 1 corresponds to ν =30GHz. When an external magnetic field is applied to the sample, the degeneracy is lifted and the eigenstates acquire additional energy according to their m-projection quantum number, leading to a splitting of the energy levels (Zeeman effect). In the absence of nuclear spin, m = m J = J, J +1,...,J 1,J,takes2J +1 values; in the presence of nuclear spin, and for weak magnetic field strength, each F -level is split into 2F + 1 sublevels labeled by their a The notation for the Hg isotopes in the figures is based on the pre-1970 convention, where the atomic number A = Z + N, is shown in the upper right, rather than on the lower left of the chemical symbol of the element.

4 4 Reminiscences: A Journey Through Particle Physics m F quantum number. For such weak fields the additional energy due to the magnetic field is E J = m J g J B and E F = m F g F B, (1) where g J,g F are the corresponding g-factors, and B is the external magnetic field. For the even isotopes of Hg, I = 0, and the situation is simple. Since the excited atoms are in the J = 1 state, the level splits into three sublevels that grow as B,0,B, and since the ground state has J = 0, the spectral line for the 3 P 1 1 S 0 transition depends similarly on B. For odd isotopes, every hyperfine level splits into 2F + 1 sublevels at low fields. However, when the interaction energy E becomes comparable to the hyperfine splitting, the coupling to the electron s angular momentum dominates, and the energy levels follow the m J quantum number, but each such level is split further into 2I + 1 sublevels. This is shown in Fig. 1.2 for 199 Hg where I =1/2. We are now able to describe the double optical resonance experiment. It is based on the concept of optical pumping, but at a time when tunable lasers were not available. In the absence of a laser, the exciting radiation was provided by an electrodeless discharge (to reduce the line width) of a single isotope of Hg, 198 Hg, placed in a strong magnetic field, the scanning field. A filter was used to select Figure 1.2: Zeeman effect of the hyperfine levels of the 3 P 1 state of 199 Hg [3].

5 Level Crossing 5 the nm line, and by tuning the scanning field, the frequency of one Zeeman component of the emitted radiation could be set to a particular value. This pump radiation was incident on a Hg cell, (the sample), placed in a separate magnetic field, the splitting field. Any desired m-sublevel of the sample could be excited by adjusting the frequency and polarization of the pump radiation. The resonance radiation emitted from the sample was observed at 90 degrees relative to the incident excitation, and maintains the polarization of the pump. A schematic of the apparatus is shown in Fig Consider now a transition from the resonantly excited m-sublevel in the sample to another m-sublevel before the atom returns to the Figure 1.3: Schematic of the double resonance apparatus [4].

6 October 4, :5 SPI-B1432 9in x 6in Reminiscences: A Journey Through Particle Physics Reminiscences: A Journey Through Particle Physics ground state. The decay from this new sublevel will, in general, alter the polarization of the resonance radiation. The sample is placed in a microwave cavity, at a location where the oscillatory magnetic field H1 is maximal. When the microwave frequency equals the energy difference between the two m-sublevels, the appropriate rotating component of H1 induces transitions. The transition is detected by the appearance of the orthogonal polarization in the emitted resonance radiation. In my experiment, we used S-band microwaves (war surplus equipment) at f 3 GHz which, for 198 Hg, resonate when the splitting field is of order 0.3 T. A typical resonance signal as a function of the strength of the splitting field is shown in Fig Figure 1.4: Line shape of the signal intensity at fixed microwave frequency as a function of the splitting magnetic field [4]. b1432-ch01

7 Level Crossing 7 Au(d, 2n)80 197Hg. The Hg was then boiled off the gold foil and sealed in a quartz cell. This latter process produced some anxious The width of the line in Fig. 1.4 is 10 MHz, and it exceeds the natural width of the excited state, because the line is broadened by the microwave power. Measuring the transition frequency and the splitting magnetic field one can determine the hyperfine spacing and therefore the value of the nuclear moments. The nomenclature double resonance is now clear: the first resonance occurs when the pump radiation has been correctly selected to excite the desired m- sublevel of the sample, and the second resonance occurs when the microwave frequency coincides with the energy difference between the two m-sublevels, that depends on the strength of the splitting magnetic field. After working with natural Hg and completing an extensive study of the hyperfine structure and isotope shift [4], I turned my attention to my thesis topic, involving the investigation of radioactive 197 Hg. This metastable isotope has a lifetime of 65 hours, and, as already mentioned, there also exists an isomeric (excited nuclear) state with a lifetime of 23 hours that is labeled as 197 Hg. The nuclear decay scheme is shown in Fig The sample was prepared by bombarding gold with 15 MeV deuterons from the MIT cyclotron, using the reaction Figure 1.5: Nuclear decay scheme of radioactive 197 Hg and 197 Hg [5].

8 8 Reminiscences: A Journey Through Particle Physics moments, when the glass vacuum distillation apparatus shattered in one of our attempts to extract the mercury from the gold (reverse alchemy!). In the end, about 1 mcurie of 197 Hg, which corresponds to atoms, was loaded into the cell. This was sufficient for obtaining good double resonance signals. The radioactive samples were used to carry out successful double resonance experiments on both 197 Hg and 197 Hg, but also to take high resolution spectra of the hyperfine structure of the nm line of 197 Hg using the MIT grating spectrograph in 13 th order and also crossed by a Fabry Perot etalon. The spectroscopic work was done under the guidance of Dr. S. P. Davis, who went on to a distinguished career on the faculty at U. C. Berkeley, and with help from Professor L. C. Bradley. One of the more rewarding results was the measurement of the isotope shift of 197 Hg and its comparison to the shift in 197 Hg, which led to the quantitative establishment of the difference in the radius of an excited and ground state of an atomic nucleus. 197 Hg has nuclear spin I =1/2 and the hyperfine structure is therefore very similar to that of the stable 199 Hg isotope, but shifted due to the different size of the nucleus. On the other hand 197 Hg has nuclear spin I =13/2. Coupling of this spin to the, J = 1, total orbital angular momentum, gives rise to three hyperfine levels, with F =11/2, F =13/2, and F =15/2.Inthepresenceofanexternal magnetic field, these hyperfine levels split correspondingly, into 12, 14 and 16 Zeeman sublevels. To calculate the energy of the sublevels as a function of the magnetic field it is necessary to invert a matrix. At that time, in 1957, this was a daunting task and I therefore asked the MIT computing center to do the calculation on their recently-acquired IBM 704 computer. The result, in Fig. 1.6, shows the multitude of m F sublevels at low field, while at high field the pattern converges towards the three m J sublevels expected from the J = 1 total electronic angular momentum of the excited atomic state [5]. I was very proud of the plot and made an enlarged copy which I posted prominently in the lab. The lab was kept in running order by a gifted technician, Mr. E. Bardho. When he saw the plot, he was intrigued by the

9 Figure 1.6: Zeeman effect of the 3 P 1 level of 197 Hg [5]. Level Crossing 9

10 10 Reminiscences: A Journey Through Particle Physics convergence of most of the F =13/2 sublevels when the splitting magnetic field was B 0.8 T, and reasonably asked what would happen when that field value was reached. We decided that transitions between sublevels would take place, as in the standard double resonance experiment, and would be observable even in the absence of microwave power. The conclusion was correct, and the effect indeed occurs whenever two m-sublevels cross, provided m =0or2[7]. We set out to observe the effect by sweeping the splitting magnetic field near the calculated cross-over value, which was done by advancing with a stepping motor the contact point on a rheostat. The sweeping speed was adjusted to optimize the observable signal under normal operating conditions, that is, when the microwave power was on. We did not find a signal and soon gave up the search. The reason that we did not observe a signal was that in the absence of microwave power, the width of the transition is governed by the very narrow natural width of the excited atomic state, and given the integration time of our detection chain, the sweep was too fast to observe such a narrow line. About three months after I left MIT and was not any longer involved in atomic physics, a group at the University of Michigan led by Peter Franken published the first results on level crossing in atomic systems [6]. They used Helium, which has an electronic configuration similar to that of Hg, and observed the cross-over between m J -sublevels with m J = 0 in a moderate magnetic field. As shown in Fig. 1.7, the crossing occurred for the sublevels belonging to the 2 3 P 1 and 2 3 P 2 levels of the first excited state of orthohelium. Soon after this announcement my former colleagues returned to my apparatus, and within half an hour located the level crossing in 199 Hg [8]. The cross-over of the F =1/2, m F =+1/2andF =3/2, m F = 3/2 sublevels can be seen in Fig The advantage of this technique is that because the line is so narrow, the fine, or hyperfine, spacings can be obtained with greatly improved accuracy using the value of the magnetic field at which the cross-over occurs. The moral of this reminiscence is that, while intuition is valuable, it is not sufficient, and that it is important to understand beforehand what to expect and look for, when carrying out an experiment.

11 Level Crossing 11 Figure 1.7: Level crossing in Helium [6]. References 1. Magnets, by F. Bitter, Doubleday Anchor Books, Garden City, NY J. Brossel and A. Kastler, Compt. Rend. 229, 1213 (1949). 3. J. Brossel and F. Bitter, Phys. Rev. 86, 308 (1952). 4. P. L. Sagalyn, A. C. Melissinos and F. Bitter, Phys. Rev. 109, 375 (1958). 5. A. C. Melissinos, Phys. Rev. 11, 126 (1959); A. C. Melissinos and S. P. Davis, Phys. Rev. 115, 130 (1959). 6. F. D. Colgrove et al., Phys. Rev. Lett. 3, 420 (1959). 7. P. A. Franken, Phys. Rev. 121, 508 (1961). 8. H. R. Hirsch, Bull. Am. Phys. Soc. Series II, 5, 274 (1960).