I was calculating deuteriums magnetic dipole moment in the $l=0$ state, given the value of its quantum number $j=1$ and $j=l+s=l+s_p+s_n$. The state that we want to calculate this in is the $\left| S=1, S_z=1 \right\rangle$ state and using the Clebsches I got to:

$$ \left\langle \mu \right\rangle =\left\langle S=1, S_z=1 \right| \sum_i \frac{\hat{S_z}^{(i)}}{\hbar} \mu_{_N} g_i \left| S=1, S_z=1 \right\rangle $$

$$ \left\langle \mu \right\rangle =\left\langle S=1, S_z=1 \right| \sum_i \frac{\hat{S_z}^{(i)}}{\hbar} \mu_{_N} g_i \left| m_p= \frac{1}{2} , m_n= \frac{1}{2} \right\rangle $$

$$\left\langle \mu \right\rangle = 0.88\mu_{_N}$$

where $g_i$ represent the respective gyromagnetic moments $g_p=5.538$ and $g_n=-3.826$ and $\mu_{_N}$ is the Nuclear magneton. I know that the observed value for $\left\langle \mu \right\rangle$ is $0.86 \mu_{_N}$. How do we explain this descrepancy? Can we conclude anything about the symmetry of the nuclear potential?

I was calculating deuterium's magnetic dipole moment in the $l=0$ state, given the value of its quantum number $j=1$ and $j=l+s=l+s_p+s_n$. The state that we want to calculate this in is the $\left| S=1, S_z=1 \right\rangle$ state and using the Clebsch-Gordan coefficients, I got to:

$$ \langle\mu\rangle =\left\langle S=1, S_z=1 \left| \sum_i \frac{\hat{S_z}^{(i)}}{\hbar} \mu_{_N} g_i \right| S=1, S_z=1 \right\rangle $$

$$\langle\mu\rangle =\left\langle S=1, S_z=1 \left| \sum_i \frac{\hat{S_z}^{(i)}}{\hbar} \mu_{_N} g_i \right| m_p= \frac{1}{2} , m_n= \frac{1}{2} \right\rangle $$

$$\left\langle \mu \right\rangle = 0.88\mu_{_N}$$

where $g_i$ represent the respective gyromagnetic moments $g_p=5.538$ and $g_n=-3.826$ and $\mu_{_N}$ is the nuclear magneton. I know that the observed value for $\left\langle \mu \right\rangle$ is $0.86 \mu_{_N}$. How do we explain this discrepancy? Can we conclude anything about the symmetry of the nuclear potential?