GATE 2023 PH – Question 29
The deuteron is a bound state of a neutron and a proton. Which of the following statements is(are) CORRECT?
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Correct answer: (C) The deuteron state is an admixture of 3S1 and 3D1 states
Explanation
Check each statement about the **deuteron** (the bound state of a proton and a neutron, $J^P=1^+$).
- **A. A finite electric quadrupole moment due to a non-spherical electronic charge distribution.** False. The quadrupole moment ($Q\approx0.286$ e fm²) is caused by the non-spherical distribution of the **nuclear** (proton) charge, not electronic charge.
- **B. The magnetic moment equals the sum of the neutron and proton moments.** False. This would hold for a pure $^3S_1$ state. The actual value is slightly smaller (0.857 against 0.880 nuclear magnetons) because of the $D$-state admixture.
- **C. The deuteron is an admixture of $^3S_1$ and $^3D_1$ states.** True. The tensor part of the nuclear force mixes $L=0$ and $L=2$ with $S=1$, $J=1$. ✓
- **D. An admixture of $^3S_1$ and $^3P_1$.** False. A $P$ state has the wrong parity (odd $L$), but the deuteron has positive parity.
Answer **C**.