Sub-Doppler resolution Stark-modulation spectra of 20 transitions in the ${\nu}_{3}$ band of methane have been recorded using a difference-frequency-generation source referenced to an optical frequency comb with a frequency uncertainty of a few kilohertz. First-order Stark shifts in the vibrational excited (${v}_{3}=1$) and ground states have been measured separately in the presence of an electric field up to 31 kV/cm. The observed spectra have been analyzed, taking into account the mixing of the vibration–rotation wave functions due to high-order vibration–rotation interactions. The permanent electric dipole moment constants induced by the vibration, rotation, and Coriolis-type terms in the ${v}_{3}=1$ state, and those induced by rotation in the vibrational ground state, are determined as ${P}^{\mathrm{vib}}=-16.82(7)\text{\hspace{0.17em}}\mathrm{mDebye}$, ${P}^{\mathrm{rot}\prime}=18.6(4)\text{\hspace{0.17em}}\text{\mu}\mathrm{Debye}$, ${P}^{\mathrm{Cor}}=10.4(17)\text{\hspace{0.17em}}\text{\mu}\mathrm{Debye}$, and ${P}^{\mathrm{rot}\prime \prime}=24.47(12)\text{\hspace{0.17em}}\text{\mu}\mathrm{Debye}$.

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Numbers in parentheses indicate the uncertainties ${\sigma}_{{J}^{\prime \prime}}$ in units of the last digit. Note that the uncertainty of the electric field is not considered in ${\sigma}_{{J}^{\prime \prime}}$.

Table 2.

Stark Shift Coefficients for the ${v}_{3}=1$ State $\overline{{S}_{{J}_{R}^{\prime}}}$^{a}

Numbers in parentheses indicate the uncertainties ${\sigma}_{{J}_{R}^{\prime}}$ in units of the last digit. Note that the uncertainty of the electric field strength is not considered in ${\sigma}_{{J}_{R}^{\prime}}$.

Table 3.

Calculated Stark Shift Constants, ${C}_{{J}_{R}^{\prime}}^{\mathrm{vib}}$, ${C}_{{J}_{R}^{\prime}}^{\mathrm{rot}\prime}$, and ${C}_{{J}_{R}^{\prime}}^{\mathrm{Cor}}$, Together with ${C}_{{J}_{R}^{\prime}}^{\mathrm{vib,M}}$ [27] for Comparison

${J}_{R}^{\prime}$

${C}_{{J}_{R}^{\prime}}^{\mathrm{vib}}$

${C}_{{J}_{R}^{\prime}}^{\mathrm{vib,M}}$

${C}_{{J}_{R}^{\prime}}^{\mathrm{rot}\prime}$

${C}_{{J}_{R}^{\prime}}^{\mathrm{Cor}}$

${1}_{2}$

−0.86603

−0.86603

0

−1.7321

${3}_{4}$

0.19701

0.18558

−1.8870

1.8080

${4}_{5}$

−0.12992

−0.10392

1.8922

−1.5214

${5}_{6}$

−0.019857

−0.026243

1.1052

−0.37782

${6}_{7}$

0.095916

0.081572

−4.3004

1.8068

${7}_{8}^{(1)}$

0.0089684

0.010779

−1.1836

0.25544

${7}_{8}^{(2)}$

−0.073290

−0.057171

4.4172

−1.5968

${8}_{9}$

−0.016078

−0.019811

2.2335

−0.48182

${2}_{2}$

0.28868

0.28868

0

−1.7321

${4}_{4}$

−0.12989

−0.15588

−1.8922

1.0018

${5}_{5}$

0.082401

0.10392

2.4998

−0.55055

${6}_{6}$

0.024671

0.029457

0.75401

−0.30373

${7}_{7}$

−0.075855

−0.099416

−4.6964

0.62358

${8}_{8}^{(1)}$

−0.0076359

−0.013972

−0.42071

0.13149

${8}_{8}^{(2)}$

0.053249

0.074111

4.4254

−0.42023

${3}_{2}$

−0.052672

−0.041239

1.8870

0.79006

${5}_{4}$

0.052926

0.037790

−3.6050

−1.1501

${6}_{5}$

−0.038108

−0.028550

3.5464

0.97132

${7}_{6}$

−0.014471

−0.0088370

1.4628

0.40850

${8}_{7}$

0.042634

0.031839

−6.2382

−1.3945

Table 4.

Standard Deviations of the Least-Squares Fit in Kilohertz Unit for Three Kinds of ${H}_{\mathrm{high}}$ and Three Sets of Adjustable Parameters^{a}

Numbers in parentheses indicate the uncertainties ${\sigma}_{{J}^{\prime \prime}}$ in units of the last digit. Note that the uncertainty of the electric field is not considered in ${\sigma}_{{J}^{\prime \prime}}$.

Table 2.

Stark Shift Coefficients for the ${v}_{3}=1$ State $\overline{{S}_{{J}_{R}^{\prime}}}$^{a}

Numbers in parentheses indicate the uncertainties ${\sigma}_{{J}_{R}^{\prime}}$ in units of the last digit. Note that the uncertainty of the electric field strength is not considered in ${\sigma}_{{J}_{R}^{\prime}}$.

Table 3.

Calculated Stark Shift Constants, ${C}_{{J}_{R}^{\prime}}^{\mathrm{vib}}$, ${C}_{{J}_{R}^{\prime}}^{\mathrm{rot}\prime}$, and ${C}_{{J}_{R}^{\prime}}^{\mathrm{Cor}}$, Together with ${C}_{{J}_{R}^{\prime}}^{\mathrm{vib,M}}$ [27] for Comparison

${J}_{R}^{\prime}$

${C}_{{J}_{R}^{\prime}}^{\mathrm{vib}}$

${C}_{{J}_{R}^{\prime}}^{\mathrm{vib,M}}$

${C}_{{J}_{R}^{\prime}}^{\mathrm{rot}\prime}$

${C}_{{J}_{R}^{\prime}}^{\mathrm{Cor}}$

${1}_{2}$

−0.86603

−0.86603

0

−1.7321

${3}_{4}$

0.19701

0.18558

−1.8870

1.8080

${4}_{5}$

−0.12992

−0.10392

1.8922

−1.5214

${5}_{6}$

−0.019857

−0.026243

1.1052

−0.37782

${6}_{7}$

0.095916

0.081572

−4.3004

1.8068

${7}_{8}^{(1)}$

0.0089684

0.010779

−1.1836

0.25544

${7}_{8}^{(2)}$

−0.073290

−0.057171

4.4172

−1.5968

${8}_{9}$

−0.016078

−0.019811

2.2335

−0.48182

${2}_{2}$

0.28868

0.28868

0

−1.7321

${4}_{4}$

−0.12989

−0.15588

−1.8922

1.0018

${5}_{5}$

0.082401

0.10392

2.4998

−0.55055

${6}_{6}$

0.024671

0.029457

0.75401

−0.30373

${7}_{7}$

−0.075855

−0.099416

−4.6964

0.62358

${8}_{8}^{(1)}$

−0.0076359

−0.013972

−0.42071

0.13149

${8}_{8}^{(2)}$

0.053249

0.074111

4.4254

−0.42023

${3}_{2}$

−0.052672

−0.041239

1.8870

0.79006

${5}_{4}$

0.052926

0.037790

−3.6050

−1.1501

${6}_{5}$

−0.038108

−0.028550

3.5464

0.97132

${7}_{6}$

−0.014471

−0.0088370

1.4628

0.40850

${8}_{7}$

0.042634

0.031839

−6.2382

−1.3945

Table 4.

Standard Deviations of the Least-Squares Fit in Kilohertz Unit for Three Kinds of ${H}_{\mathrm{high}}$ and Three Sets of Adjustable Parameters^{a}