Chinese Journal of Chemical Physics  2016, Vol. 29 Issue (5): 527-532

#### The article information

Bai Jiao, Wang Hai-ling, Ni Xue, Deng Lun-hua

Isotope Shifts of Nitrogen around 800 nm

Chinese Journal of Chemical Physics, 2016, 29(5): 527-532

http://dx.doi.org/10.1063/1674-0068/29/cjcp1602035

### Article history

Accepted on: May 6, 2016
Isotope Shifts of Nitrogen around 800 nm
Bai Jiao, Wang Hai-ling, Ni Xue, Deng Lun-hua
Dated: Received on February 29, 2016; Accepted on May 6, 2016
State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
Abstract: The Doppler-limited absorption spectra of 14N and 15N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging molecular nitrogen buffered with helium in a homemade discharge tube. The isotope shifts of four multiplets (3s4PJ→3p4DJo, 3s4PJ→3p4PJo, 3s2DJ→5s2PJo, and 3p2PJo→5s2DJo) were measured and their J-dependent specific mass shifts were observed and discussed.
Key words: Doppler-limited absorption spectra     Isotope shifts     Specific mass shifts     J-dependence
I. INTRODUCTION

The isotope shifts (ISs) of atoms are needed in astrophysical studies such as the analysis of the quasar absorption spectra. By comparing the theoretically calculated and experimentally measured isotope shifts, it can be found that the change in the nuclear charge distributes from one isotope to another [1]. The study on the relative isotope abundance has many uses terrestrially, since various geological and biological processes tend to favor one isotope over another, it can help scientists to discover the chemical evolution of the universe. However, the IS parameters are limited and the IS characters are not well known for many atoms. The ISs of nitrogen atom are the topic of this study.

Holmes first observed a bunch of the isotope shifts of 3p4PJ°→3s4PJ, 3p4SJ°→3s4PJ, and 3p2PJ→3s2PJ° transitions of 15N-14N isotopic pair using a Fabry-Pèrot interometer [2]. In Holmes' experiment, no hyperfine structure in any component has been observed. After Holmes' work, several groups have reported the isotope shifts in some lines of nitrogen [3-7]. Cangiano studied the hyperfine structures and isotope shifts of 3s4PJ→3p4PJ° transitions using an external cavity diode laser and Doppler-free techniques [4]. Jennerich later reported the high-resolution saturation absorption spectra of 3s4PJ→3p4PJ° and 3s4PJ→3p4DJ° transitions [5]. Jönsson calculated the hyperfine structures of 14N and 15N using ab initio multiconfiguration Hartree-Fock method [6]. However, the hyperfine constants of 3s4PJ→ 3p4PJ° and 3s4PJ→3p4DJ° transitions from Jönsson's theoretical calculation are strongly inconsistent with these from Jennerich's experiment. Carette et al. studied the saturation spectra of the low lying states of N I [7], their results are in agreement with Jönsson's theoretical ones.

A possible J-dependent specific mass shift of atomic nitrogen was found in some studies [2, 4-7]. However, the complete ISs of the involved multiplets were not measured. Here, we report our complete study on the ISs of 3s4PJ→3p4PJ° and 3s4PJ→3p4DJ° transitions, and some observed ISs on 3s2DJ→5p2DJ° and 3p2PJ°→5s2PJ transitions of atomic nitrogen. The J-dependent specific mass shifts of these multiplets were confirmed and discussed.

II. EXPERIMENT

The experimental apparatus used in this work is illustrated in Fig. 1, which is similar to that has been described previously [8, 9]. A single-mode Ti:Sapphire laser (Coherent Ring 899-29) pumped by a Nd:YVO4 laser (Coherent Verdi-10, at 532 nm) was used as the excitation source. The laser beam passed through a home-made glow discharging (discharged at 23 kHz) absorption cell, which was made of a 60 cm long glass pipe with an internal diameter of 1.5 cm, then focused into a P-type layer/intrinsic layer/N-type layer (P-I-N) detector (Electro-Optics Technology, EOT-2030A). The output signal of the detector was demodulated using a lock-in amplifier at 2×23 kHz (concentration demodulation). Finally, the signal was acquired and processed by a computer to obtain the spectra of 14N and 15N. The nitrogen atoms were generated by discharging the mixture of trace 14N2, 15N2 buffered with helium (200 Pa). The absolute wavenumbers were determined by simultaneously recording the Doppler-limited absorption spectrum of I2 [10]. The absolute wavenumbers were determined to an accuracy of ±0.007 cm-1.

 FIG. 1 Schematic of experimental setup.
III. RESULTS AND DISCUSSION

Totally, we measured ISs for 20 transitions of 4 multiplets of nitrogen atoms. In the experiment, the volume ratio of 14N, 15N to helium mixture was properly prepared so that the spectra of two isotopes could be measured simultaneously with comparable intensity.Figure 2 shows partial of the absorption spectra that were fitted to extract the isotope shifts of nitrogen. The spectra of 14N were individually measured to distinguish 14N from the twin peaks of the IS spectra. Figure 2(a) shows the spectrum of 3s4P5/2→3p4D°3/2 transition, the peak at shorter frequency is 15N, while the peak at longer frequency is due to the transition of 14N. Figure 2(b) is the spectrum of 3s2D3/2→5p2D°3/2 transition, the peak at lower frequency is 14N, the peak at higher frequency is due to the transition of 15N. The exact line centers of absorption spectra were obtained by fitting the spectra with Gaussian functions and shared line widths. The residuals between the experimental data and the Gaussian fitting are given in Fig. 2. The full width at half maximum (FWHM) of these lines is around 1000 MHz, which is comparable to the Doppler broadening of this experimental system.

 FIG. 2 Absorption spectra of (a) 3s4P5/2→3p4D°3/2 and (b) 3s2D3/2→5p2D°3/2 transitions of 14N and 15N. The black dot lines are our experimentally measured spectra, the red solid lines are the Gaussian fitting of the whole experimental spectra, pink and blue solid lines are the Gaussian fitting of the 15N and 14N spectra, the green solid lines are the residuals between the experimental data and the Gaussian fitting. In (a), the left peak is 15N signal, right peak is 14N, the value of IS ((v(15N)-v(14N)) is negative; In (b), the left peak is 14N signal, right peak is 15N, the value of IS is positive.

The isotope shift of nitrogen is the difference in the atomic spectra between 14N and 15N. It comes from two sources: the finite size of the nuclear charge distribution (the field shift, FS), and the finite mass of the nucleus (the mass shift, MS) [11, 12]. In first-order perturbation theory, the IS can be described as [13]:

 (1)

The contribution from second source is traditionally divided into two parts: the normal mass shift (NMS) and the specific mass shift (SMS).

 (2)

The NMS is calculated in a straightforward way from the wavelength of the optical transition of 14N [14].

 (3)

where, $m_\textrm{e}$ is the electron mass, $m_\textrm{p}$ is the proton mass, vexptis the experiment wave number of 14N in cm-1, $A'$ is the mass number of 15N, A is the mass number of 14N. The residual isotope shift (RIS) will be written as:

 (4)

The isotope shift values extracted out from experimental spectra are listed in Table I, along with those from literatures. The sign assigned to the isotope follows the rule that a shift to higher frequencies in going 14N to 15N is positive. In Table I the signs of the ISs of 3s2DJ→5p2DJ° and 3p2PJ°→5s2PJ are positive which have the same sign as the reported ISs of 3s2P3/2→3p2P°1/2 in Holmes' measurement [2], the ISs of 3s4PJ→3p4DJ° and 3s4PJ→3p4PJ° are negative which are the same as previous investigation [6-8]. The NMS values were calculated using Eq.(3), so the uncertainties will not be given here.

Table I Summary of the isotope shifts of 14N and 15N around 800 nm. “Measured IS”=v(15N)-v(14N), where v(15N) and v(14N) are the measured line-centers of the atom spectra. The NMSs are calculated from the experimentally measured ISs. The uncertainties for our experimental data are one standard deviation of the mean.

The measured isotope shifts of 3s4PJ→3p4DJ° transitions are listed in Table I and compared with the results measured using saturated absorption spectroscopy [5], and with those measured with Doppler limited spectroscopy [2, 3]. Our results show good agreement with Jennerich's measured ones [5]. We measured the ISs of all eight transitions, and also gave the systematic IS and NMS values.

The measured isotope shifts of 3s4PJ→3p4PJ° transitions are also listed in Table I and compared with the results from Jennerich et al. [5], Cangiano et al. [4], and Holmes [2, 3]. Our results are close to Jennerich's results [5]. Our results are also close to Cangiano's results [4] except a large difference in 3s4P3/2→3p4P°5/2 transition.

Holmes reported the IS of the 3s2PJ→3p2PJ° transitions [2]. However, we could not obtain high quality spectra to get the IS of this multiplet. Jennerich et al. [5] and Cangiano et al. [4] did not report these IS values. Here, we cited Holmes' results in Table I for further analysis. We also measured some ISs of 3s2DJ→5p2D°J and 3p2PJ°→5s2PJ, these values were newly reported as we know. Unfortunately, not all the fine structure transitions were observed.

In our work, the measured residual isotope shifts (RIS=IS-NMS) vary from -2781.7 MHz for 3s4P5/2→ 3p4D°7/2to -2487.3 MHz for 3s4P1/2→3p4D°1/2 and from -2856.6 MHz for 3s4P5/2→3p4P°5/2 to -2549.6 MHz for 3s4P1/2→3p4P°1/2. From Eq.(4), the RIS comes from two components, the SMS and the FS. The FS depends on the variation of the electron density inside the nuclear charge distribution. As a general rule, for light atoms (Z<30) the mass shift is the dominant contribution while for heavy atoms (Z＞60) the field shift plays the main role. The ab initio calculation of Jönsson et al. [6] gives the estimated value of FS around 0.2 MHz for these considered transitions. Thus for nitrogen, the FS can be neglected in the present work and the dominant part in RIS is SMS.

The schematic energy level diagram of the 2p23s4PJ→2p23p4PJ° and 2p23s4PJ→2p23p4DJ° transitions is shown in Fig. 3. The transitions were assigned base on the data in NIST's database. The transition frequencies are extracted from our experimental data. From Fig. 3, we can give the difference between two energy levels. For instance, the difference between the observed transitions in lines 3s4P5/2→3pD°7/2and 3s4P5/2→3p4D°5/2gives the difference between the energy levels of 3p4D°7/2and 3p4D°5/2.

 FIG. 3 Schematic energy level diagram of the 2p23s4PJ, 2p23p4PJ° and 2p23s4DJ° states, and the observed transitions between these states around 800 nm.
A. 3s4PJ→3p4LJ° (L=P or D) transitions

Table II listed the experimentally measured specific mass shifts of 3s4PJ→3p4PJ° and 3s4PJ→3p4DJ° transitions. The field shifts are neglected. In Table II, the lines of a multiplet do not exhibit the same isotope shifts and the shifts in the energy levels depend on the J-value. That is due to that the involved transitions of nitrogen atom are not a case of pure Russell-Saunders coupling, the shifts are J-dependence.

Table II Specific mass shifts (in MHz) of the transitions of 3s4PJ"→3p4L°J'. The field shifts are neglected.

Holmes [2] first listed some J-dependence for the 3s4PJ° terms of nitrogen, for example the ISs measured difference relative to 3s4P5/2→3p4P°5/2and 3s4P5/2→3p4P°3/2is 51(33) MHz. Cangiano et al. [4] reported some J-dependence for the SMS of 3p4PJ° term, they obtained 110(300) and 318(300) MHz for the SMS differences 5/2-3/2 measured relative to 3s4P5/2and 3s4P3/2, respectively. We got SMS differences of 41(20) and 62(18) MHz for these two levels respectively. Carette et al. and Jennerich et al. gave differences of 1.0(35) and -32.0(32) MHz with respect to the level 3s4P5/2. We obtained -48(17) and -26(41) MHz for the SMS differences 3/2-1/2 measured relative to 3s4P3/2 and 3s4P1/2, respectively. Only Cangiano et al. found a difference of -52(300) MHz for the level of 3s4P3/2.

In the case of the 3p4DJ° term, Jennerich [5], Carette [7], and this work obtained -14.73(100), 1.77(102), and -13(20) MHz for 7/2-5/2 SMS differences of 3s4P5/2, respectively. We also gave 13(34) and -13(18) MHz SMS differences for the 5/2-3/2 related to 3s4P5/2and 3s4P3/2, 17(35) and -3(14) MHz for the 3/2-1/2 with respect to 3s4P3/2and 3s4P1/2, respectively.

The experimental results of Cangiano et al. [4] showed a large J-dependence of the 3p4DJ° and 3p4PJ° states. Carette et al. [7] argued that the results from Cangiano et al. [4] are affected by a wrong assignment of the spectral lines. Our measured concentration modulation absorption spectra and Jennerich's saturated absorption spectra gave the SMS differences which are in the range 3-62 MHz. Carette's [7] saturation spectra gave a small J-dependence of these states. The results of Carette, Jennerich and present work exhibit small J- and L-dependence of the SMS for the 3p4L° (L=P and D) upper states. However, the limited relativistic ab initio calculations estimate a J-dependence of maximum 1 MHz [7] for 3p4L°, which is an order smaller than our and Jennerich's results. Thus, more accurate experimental and theoretical results need to be proceeded by different methods.

For the lower 3s4PJ term, Cangiano et al. gave the values of -340(300) and -548(300) MHz for the SMS differences between 3s4P5/2and 3s4P3/2sharing the same 3p4P°3/2 and 3p4P°5/2, respectively. Our work gave the values of -146(13) and -167(25) MHz for the SMS difference related to 3s4P5/2-3/2, and -104(30) and -82(28) MHz for the SMS differences related to 3s4P3/2-1/2.

The SMS difference between the different J-values of the lower levels are larger than those between the different J-values of the upper levels in 3s4PJ→3p4LJ° transitions. This result is the same as that of Carette's [7].

B. 3s2DJ→5p2DJ° and 3s2PJ→3p2PJ° transitions

Table III listed the specific mass shifts of 3s2DJ→5p2DJ° and 3s2PJ→3p2PJ° of 14N and 15N. The values deduced from our data and that deduced from Holmes' analysis are shown.

Table III Specific mass shifts of the transitions of 3s2DJ"→5p2D°J" and 3s2PJ"→3p2P°J'. The field shifts are neglected.

The measured SMS difference between the upper levels 5p2D°5/2and 5p2D°3/2is -229(66) MHz, and the one between lower levels 3s2D5/2and 3s2D3/2is 99(39) MHz in present work. In Holmes' experiment, he measured the values of -276(66) and -222(45) MHz for the SMS difference between the upper levels 3p2P°3/2and 3p2P°1/2sharing the same 3s2P3/2and 3s2P1/2, respectively. He also gave the value of 54(51) and 108(60) MHz for the SMS difference between the lower levels 3s2P3/2and 3s2P1/2sharing the same 3p2P°3/2 and 3p2P°1/2. Holmes' and our results show that SMS difference between the different J-values of the lower levels and those between the different J-values of the upper levels of the 3s2DJ→5p2DJ° and 3s2PJ→3p2PJ° transitions are small compared with that of 3s4PJ→3p4LJ° transitions.

Cangiano et al. pointed out the J-dependence of the RIS values have been attributed by Keller et al. [15] to relativistic contributions and electron correlations affecting the SMS. The J-dependence of IS results from the higher-order IS effect, i.e., the so-called crossed-second-order (CSO) effect or the far configuration-mixing effect [16]. The CSO effect between the magnetic interaction and IS operators leads to the J-dependence of IS in a term of the pure configuration. In Jennerich's report, he argued that identification of these effects has generally been limited by the availability of experimental data. SMS measurements reveal the nuclear shell very distinctly, the structure at magic numbers can cause striking anomalies in the behavior of the IS of nitrogen.

IV. CONCLUSION

We systematically measured the isotope shifts spectra of 14N and 15N around 800 nm by using concentration modulation absorption spectroscopy. By analyzing these experimental data, we obtained the ISs between the two stable isotopes of atomic nitrogen. Our experimental results are close to other groups' results using saturated absorption spectroscopy method. The SMS value of 3s4PJ→3p4DJ° transitions coming from the 3s4P5/2level is around 200 MHz larger than these coming from the 3s4P3/2level, and around 300 MHz larger than these coming from the 3s4P1/2level. For 3s4PJ→3p4PJ° transitions, we can see the similar result. It may be concluded that the J value of the lower level 3s4P has a dominant contribution to the SMS values in both the 3s4PJ→3p4PJ° and the 3s4PJ→3p4DJ° transitions. The larger J value in 3s4P level is, the larger IS value of the transition is. Similar phenomenon can be seen in Jennerich and Carette's results. For 3s2DJ→5p2DJ° transitions, the J value of the upper level 5p2DJ° has dominant role in the SMS values. The larger the J value is, the smaller the IS value is. Holems' experimental data show the similar result for the 3s2PJ→3p2PJ° transitions. These results may be useful for comparing with highly red-shifted quasar absorption lines of nitrogen atom in order to obtain the fine structure constants, and can be used as a comparable experimental data for performing theoretical calculations on the anomalous isotope shift behavior in N atoms.

V. ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (No.61205198).

 [1] Heilig and A. Steudel K, At. Data Nucl. Data Tables 14 , 613 (1974). DOI:10.1016/S0092-640X(74)80006-9 [2] R. Holmes J, Phy. Rev. 63 , 41 (1943). DOI:10.1103/PhysRev.63.41 [3] R. Holmes J, J. Opt. Soc. Am. 41 , 360 (1951). DOI:10.1364/JOSA.41.000360 [4] Cangiano P, Angelis M, Gianfrani L, Pesce G,and Sasso A, Phys. Rev A50 , 1082 (1994). [5] M. Jennerich R, N. Keiser A,and A. Tate D, Eur. Phys. J D40 , 81 (2006). [6] Jöhsson P, Carette T, Nemouchi M,and Godefroid M, J. Phys B43 , 115006 (2010). [7] Carette T, Nemouchi M, Jöhsson P,and Godefroid M, Eur. Phys. J D60 , 231 (2010). [8] J. Wang R, Q. Chen Y, P. Cai P, J. Lu J, Y. Bi Z, H. Yang X,and S. Ma L, Chem. Phys. Lett. 307 , 339 (1999). DOI:10.1016/S0009-2614(99)00562-X [9] H. Deng L, Y. Zhu Y, L. Li C,and Q. Chen Y, J. Chem. Phys. 137 , 054308 (2012). DOI:10.1063/1.4739466 [10] IODINESPEC4, Toptica Photonics, Munich, Germany (http://www.toptica.com). [11] Sobel'man II, Introduction to the theory of atomic spec-tra. New York: Springer-Verlag (1986). [12] H. King W, Isotope Shifts in Atomic Spectra. New York: Plenum Press (1984). [13] Bender D, Brand H,and Pfeufer V, Z. Phys A318 , 291 (1984). [14] G. Li J, Nazé C, Godefroid M, Gaigalas G,and Jönsson P, Eur. Phys. J D66 , 290 (2012). [15] C. Kelley J, J. Phys B6 , 1771 (1973). [16] Bauche and R. J. Champeau J, Adv. At. Mol. Phys. 12 , 39 (1976). DOI:10.1016/S0065-2199(08)60042-1